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I mostly run GURPS, but I cut my teeth on D&D 3rd Edition, and I’ve learned a lot of tricks over the years for running fast combat.Analog vs DigitalI ban electronics at my table. That’s one of the simplest steps to aid player engagement. Without the magic thinky-box to distract, there’s nothing to pay attention to but the game.Between TurnsThe very first thing to do is to explain to your players that their turn is not the time to decide what to do. They should be making those decisions on everyone else’s turns, so when it comes back around to them they should be telling you what they’re doing.I’ve stumbled on a small linguistic trick to help with this. I no longer ask players what they’d like to do. I ask them what their character is doing.Also, make sure they keep cross-talk to a minimum. Nothing slows down combat like an unrelated conversation on the side.Raziene Davis's answer to In Dungeons & Dragons, do I have to pay attention to the game, even when it's not my turn?PlanningRelated to this is the fact that combat is not the time to plan. I don’t mind at all if the players want to spend half an hour planning an ambush before it goes off, but once the arrows are flying nobody is allowed to stop play to plan. You can certainly shout “Fireball the shaman!” at your wizard as a free action, and I’ll let you take your whole turn to coordinate and communicate to everyone else, but what you certainly are not going to do is stop the game and spend half an hour planning how to react with the perfect first turn after you’ve been ambushed.EnforcementI have a pretty straightforward way of enforcing this too. If you take too long to tell me what your PC is doing, then he’s frozen in shock and does nothing that turn. This can sometimes annoy players who are new to my style, as they’re used to taking forever, but I’ve never had anybody not eventually adjust and appreciate the speed at which I run combat.Now “too long” is a bit subjective. You don’t want to punish your players. They don’t need to respond in an instant. If someone is consistently taking too long, or trying to stop play to plan, you can break out a sand-timer or something. You can get them for any length of time, but I recommend between 15 and 30 seconds. Again, the goal isn’t to punish them and rob them of their turn, but to get them doing something useful.A decent action now is better than the perfect action in ten minutes after everyone is riddled with arrows.Information Organization-PlayersThe internet tells me that this is the 5E character sheet (I’ve not played 5E yet), which I assume is the edition you’re running.https://media.wizards.com/2016/dnd/downloads/5E_CharacterSheet_Fillable.pdfI think this is a sub-optimal design. Here is the old 3rd Edition sheet.It is, I think, a bit better, as it puts almost all of your offensive information in the bottom left corner. AC and HP should be there too, but it’s better.Better yet is the current version of my home-made character sheet for GURPS.I specifically designed it so that 90% of everything you need to know for combat is right here on the first page. Basic stuff at the top. Advantages and disadvantages, which can affect combat next, then offense and defense.Here’s a snippet of the spell’s page from my homemade Pathfinder sheet for the last spellcaster I played.Frankly, I’m very bad at spellcasters and have the devil of a time remembering everything, so I made this sheet for myself. You can see on the left is the name of the spell and the absolutely vital information about it. Other important but less vital data is across the top, and then the whole freaking spell description if I’ve really forgotten what it does. Yes, there is some redundancy of data, but I don’t care.Formatted this way, I can quickly check through my spells between my turns and figure out which one I want to use.Now you can organize your own sheets how you like, but I suggest prioritizing all or almost all combat data on the front page in a clear, simple way, and either having a spell list like mine, or using spell cards, or whatever else presents the information quickly and clearly.Information Organization-Dungeon MastersThere’s also something you as the DM can do. There are really only three things in D&D you need to know about monsters in combat.Damage dealtACHit PointsI’m in the process of making Monster Cards for a GURPS game I’m planning, and here’s an example.This is meant to be folded in half and hung over my GM’s screen, so the players can see the beastie and I have my notes right in front of my fave. Gurps is a bit crunchier than D&D frequently, but you can see how I’ve mimicked my character sheet organization, and once again highlighted offense and defense in red and blue. I’m contemplating simplifying it further, but for D&D I would at least highlight across the top of a card Damage, AC, HP. You can put anything else you need below that, as the critical things are where you can find them the easiest.InitiativeThere are a couple of ways you can run initiative too. The least disruptive to D&D as written is this. Have your players roll their initiative, and write them out on a bit of scrap paper highest to lowest, but leave spaces between them. Then roll initiative for the monsters once. If that roll his higher than the highest PC, the monsters go first. If not, they go second. And then just divide the number of monsters by the number of PCs, and mix them between the party members.As an example, PCs roll high, so my initiative order looks like this.PC1Mook 1Mook 2PC2Mook3PC3Mook4Mook5I find this creates an exciting back and forth between the monsters and the PCs. If you can’t divide the mooks evenly, I would bias the smaller block of them towards the middle or top, to give the party a chance to kill them before they can act.The other reason I like this method is because at some point you should have two PCs acting one after the other, and they’ll get excited because they’ll realize they’ve killed a bunch of monsters!Make Combat Deadlier!D&D has always suffered from bullet-sponginess, and that’s something I find I dislike. In contrast, GURPS is freaking deadly. And honestly, I get tired of stabbing something for the fifteenth time if we’re just mechanically knocking down hit points.Just don’t give anything a Constitution bonus when it gets more Hit Points. I think this is already an optional rule in 5E, but it should allow you to reduce the hit points of everything, speeding up combat, without unbalancing anything. Everything dies faster now.Another option, especially if you want to have a swarm of something, is to give everything 1 HP. On any attack roll that hits, it dies. So you can swarm your players with goblins, and present a genuine threat because there’s a fuckpile of the little bastards, and they’ll feel sort of cool scything through them, right up until they run into the big daddy hobgoblin (with normal HP).Put your Finger on the ScaleYour players have no idea just what AC, HP, whatever, a particular monster has. Remember, the Monster Manual is a guidebook, not holy writ. And I’ve recently taken to the idea of “banning” the monster manual if I ever run D&D again. Sure, you can use the stat-blocks, just reskin them as something else. Dollars to donuts your players have no idea what the stat block for a chort is.With that in mind, if it would be really cool/dramatic/exciting/cathartic for the monster to die now rather than in six more turns of grinding away, then it dies now, ideally as the follow-on to a really good roll.Turn 12 of combatPaladin: I rolled 18, that hits right?Yup. Roll damagePaladin: Ugh. Three.Okay, Druid, you’re up.Druid: Nat twenty! For…twentysix points![Noticing everyone is just burnt out on this monster, they’re definitely going to kill it, it’s just taking forever and it’s got 35 points left.]Ouch, you nailed it. So, how do you want to do this?Druid: I killed it?!Yup!Murphy Barrett's answer to Can a DM cheat at D&D?Roll Attack and Damage togetherSpeaking of rolling, have your players roll their damage dice along with their attack roll. If they hit it saves just a bit of time. Do the same yourself as well.Boosted CriticalsNormally the dice (but not the modifiers) are doubled in a critical hit, but nothing feels worse than rolling a critical, but rolling a 1 for damage. My recommendation is that you just roll normal damage, plus the full value of any dice that would be doubled.So if you crit and you normally roll d12+3, instead of rolling 2d12+3, you roll d12+12+3. That way, at the very worst your critical hit does a bit more damage than your normal max, and possibly a lot more. Your players will feel badass, and it can finish the fight a bit quicker.Don’t Map EverythingYou don’t need a mini-map and figures for every combat, you can use theater of the mind. Especially for short or small fights. I do like maps for the big final battle, but there are many times where precise positioning doesn’t actually matter all that much. Don’t waste time breaking out the map for those.Murphy Barrett's answer to How do you run battles in DnD 5E without maps and minis? How does "Theatre of the Mind" work when you need to know exactly how far away an enemy is for ranged combat or spellcasting? Doesn't it get confusing if you can't see where everyone is?Murphy Barrett's answer to How do minis change Dungeons & Dragons? What are the pros and cons of using them in your D&D game?Don’t roll EverythingThere are times when you just shouldn’t roll dice. This is mostly an out of combat thing, but keep it in mind for combat too. The short version is, don’t roll dice when the only penalty for failure is just a reroll, when the PC really should know or be able to do the thing, or when something must happen for the story to continue. And if a player insists on rolling, or you want to mask that success was pre-ordained, use the roll to determine the flavor of the event, not the actual outcome.To Roll or not to Roll…Let’s say your player wants to climb up on the table. Nobody is grabbing him, there’s nothing obstructing him, just let him up on the table. Now granted, sometimes you can have a lot of fun if someone botches a roll, slips on a plate, and goes crashing ass over teakettle into the barmaid, but if combat is already dragging just skip the roll.No Checking Rules During Combat!Everyone should know the rules for how their characters work. It’s okay to rely on them a bit if you don’t have everything memorized and they’re honest players. If there’s a question on rules, remember rule zero. Dungeon Master is spelled G O D.Make the best ruling you can now, keep the ball rolling, and after the session look the rule up proper. It’s okay to email your players later and tell them you goofed, and that going forward it’ll work this way instead. But don’t retcon, especially if it takes away from your players. If you goofed, and that’s the only reason they pulled off something cool, don’t say “Okay, the rule actually works this way, so you didn’t do the thing.” Nope. What’s happened has happened. They still did the cool badass thing, it’ll just work differently/correctly next time.And trust me, any decent player won’t get bent out of shape by this. I’ve been running games for around fifteen years, and in the last game I ran I made a terrible call. In fact, I permitted something that was expressly forbidden by the rules as written. Basically I could not have been more wrong. No big deal, I just emailed my players, mea culpa, and henceforth we’re doing it per the rules as written.Now, you can’t memorize everything, which is what your GM screen is for. Keep your most vital notes on it. Also, it is actually okay to check a rule provided that you know where to find it. Basically, if it takes more than 30 seconds to find, make a ruling and move on.Keep the Action InterestingDon’t just keep slamming goblins into the party until something dies. Remember tactics are a thing. Use terrain, use tricks, make sure the party never has the same fight twice.Maybe the goblins attacked, but then start to withdraw right away…to draw the players into an ambush. Maybe they have an alchemist who starts tossing magic bombs…that are powerful hallucinogens. Maybe the goblins are on their way home from a long day of murder and mayhem, and the party has completely surprised them. The first goblin goes down, and the rest panic and run off screaming whilst flailing their arms over their heads.Remember, it’s quite unusual for a group to continue to fight until they’re all dead. Historically some forces have retreated after as little as 10% casualties.XP is for Problem SolvingRelated to the above, don’t give players XP just for killing everything, award it for solving problems. If the job is to deal with the goblins, driving them off or hiring them to protect the village from the ogres solves the problem just as well as killing them. Full XP!What this does is allow your players to be creative. If they don’t have to kill everything, they may decide to “win” by deliberately spooking the enemy so they run away. Or whatever else occurs to them.Murphy Barrett's answer to What are different objectives that can be given to players during D&D combat other than kill all the monsters?Roll with it!Remember that role-playing games are collaborative story-telling. It’s not 100% on you to control the action. The players get a vote, and the more you can work with what they give you, the more fun everyone is likely to have.I don’t like to say “no” to my players if I can help it, though I’m perfectly fine letting them live with the consequences of their actions. So if the bard wants to climb up on the chandelier, swing across the great hall, and try to stab the guards in the process…well, there’s nothing that actually stops him from trying, so let him have a go at it.That’ll surely keep combat interesting, no matter how it turns out.PCs DieSo if your erstwhile Errol Flynn gets himself skewered, well…it’s unfortunate, but people die. I dislike PC death, but sometimes it happens, and without the risk of death many games eventually feel hollow as there’s no real risk.Murphy Barrett's answer to As a D&D GM, are you inclined to let a player die? Or do you bend the rules to let them live?Murphy Barrett's answer to How can you prevent Dungeon Masters from creating "Everybody Dies" situations when the players do something unexpected?Set the SceneRemember that you’re supposed to be a storyteller. Make combat feel vital and exciting, and even if it takes a while the players will be riveted.For the most part, combat will be fairly straightforward. But be alert and open to moments that can be memorable or interesting. It can be simple things.“You did how much damage? Okay, he’s dead.”vs“You did how much damage? Okay, your arrow hits him squarely in the back and he drops like a sack of potatoes.”Murphy Barrett's answer to How do I narrate combat as a dungeon master?Command PresenceI don’t just mean you’re physical presence at the table, being a good Dungeon Master is a nearly continuous improvisational performance while also being in command of a detail of cats hopped up on Cheetos and Mountain Dew.When I was younger I hated public speaking. Many folks do. But it turned out I have three particular nervous habits that are very useful when public speaking.I get loudI paceI gesticulateThese are all things that hold people’s attention.So when you’re GMing, learn to project your voice. You don’t want to shout, that’ll strain your vocal cords, but, like an opera singer, you want to learn how to fill a room with your voice.Study good orators, from other DMs to stand-up comedians to your grandfather telling you stories that hold your rapt attention. Maybe even go to an improv class if you have the time, money, and interest. But listen to how people tell good stories, and emulate them.You are, quite frankly, a real-life bard.Now, this is not to say you have to be Matt Mercer. Matt Mercer is a professional, with a budget and staff. In fact, do not be Matt Mercer. You can learn from him, but be the best you that you can be.Murphy Barrett's answer to How can I accommodate one of the players in my D&D campaign who asked if I could act and DM more like Matt Mercer? in The Dungeon DeepLearn when to speak boldly, as the enemy barbarian challenges the Paladin to single combat, or pitch your voice low as the goblins sneak up on the party, or rasp it just right as the demon taunts them.Of course, you don’t actually have to do all this, or at least not yet. These are things I try to do because it keeps may players engaged and I enjoy it. But at the very least, don’t be a wilting flower behind the GM screen. Be able to speak with authority, be able to tell someone to knock-off the cross talk, be able to tell a player “well, there’s no rule for that…but you know what, roll me X to see if you pull it off”, and be able to have fun and be engaged yourself as you lead this collaborative storytelling effort. If you’re interested and excited that at the very least will tend to keep your players excited and interested.Now go forth and give your players glorious fights that will be celebrated with wine and song. And should they fall, rejoice at the sound wings as the Valkyrie come to bring them to Valhöll.Original question-I'm playing D&D with some relatively new players (somewhat new myself), and combat is taking ages. How do I speed it up?

What don’t they tell you about being a genius (IQ 144+)?Who is/are “they”?IQ does not precede Genius, Genius precedes IQ.If you have an IQ of 144+, you are not a Genius, you are someone with an IQ of 144+.If you become recognised as a Genius, it will probably be because you revolutionised your field of endeavour. Examples of this phenomenon are Newton, Einstein, Faraday, Edison, Kant, Wittgenstein.When that happens, please inform us all.To be certain of your IQ rating try this little test. You may use reference books to assist you. You may take as long as you wish. I have completed this test (send your answer sheet to me and I will mark it free of charge - contact me through Quora):Level I1) In 1976 Marcelo was 11 years old. How old will he be in 1999?2) If 13 bullets cost $3.90, how much do 31 bullets cost?3) A box measures 60 cm x 50 cm x 30 cm. What is the maximum number of smaller boxes measuring 10 cm x 10 cm x 10 cm that fit in it?4) 12 people do a job in 12 days. How many people are needed to do the same job in 1 day?5) A collection consists of 12 volumes. There are 300 pages in each volume, 50 lines on each page, and 100 letters on each line. What is the total number of letters in the collection?Level II6) A company has enough stock to supply its clientele of 2,500 people for 12 months. How long would this stock last if the clientele grew to 6,000 people?7) If one horse can pull 600 kg, how many horses are needed to pull 6,150 kg?8) Fernanda’s and Andreia’s ages total 18 years. What are their individual ages, given that Andreia is twice as old as Fernanda?Level III9) Ricardo weighs 30% more than José. If Ricardo were to lose 10% and José gain 20% of weight, which one of them would weigh more after that. Explain.10) A planetary system has, in addition to the main star, 9 planets. Each planet has 7 primary satellites. One out of every 21 primary satellites has 3 co-orbital satellites. How many celestial bodies are there all together?11) On a staircase with 1,000 steps there was 1 gram of gold on the 1st step, 2 grams on the 2nd, 3 grams on the 3rd, 4 grams on the 4th, 5 grams on the 5th and so on, so that there was 1 kg of gold on the last step. Given that 1 gram of gold is worth 11 dollars, calculate the total value of the gold on the staircase (in dollars).Level IV12) 99% of the people in a room are men. How many men would have to leave the room in order for this percentage to decrease to 98%? It is known that the number of women in the room is 3.13) On a chessboard with 64 squares (8 x 8), two kings can occupy 3,612 different positions. How many different positions can two kings occupy on a chessboard with 117 squares (13 x 9). Two kings may not be on the same square at the same time or occupy adjacent squares.14) Marcelo had apples, half of which he gave to his brother. The latter gave 75% of the apples that he had gotten to be equally shared between his three cousins: Anderson, João and Mané. Anderson bought 7 apples more and gave half of all his apples to his brother Mané. Mané’s apples then totaled 17. How many apples did João get?15) Maria went to a farm to buy eggs. Returning home, she gave half of them to her sister who, in turn, gave a third of those she had gotten to her boyfriend. The latter, after eating one third of the eggs that he had gotten, gave the rest to his cousin. Given that each egg weighs 70 grams, that Maria cannot carry more than 2.5 kg, and that the eggs were raw, calculate how many eggs the cousin of Maria’s sister’s boyfriend received.16) The mayor João and an important bachelor businessman, called José, held a large barbecue. Aside from the businessman José, the mayor João and his wife, the number of people present equaled the number of 100 dollar notes that the mayor spent multiplied by the the number of 100 dollar notes that the businessman spent. Given that, on average, every person consumed the equivalent of US$6.40 and that the mayor invested US$1,700, calculate how much the businessman José invested. (Note: the businessman José, the mayor João and his wife took part in the consumption)Level V17) A Formula-1 race car is racing around a circular track, completing the first lap in 3 minutes with an average speed of 144 km/h. In what time must a second lap be driven in order for the average speed of the two laps to increase to 300 km/h?18) When Antônio looked at his watch, he noticed that the hour hand was lying exactly over the minute hand. What time will it take for this to happen again? (both hands move at constant rates)19) A train with 2 cars is traveling at a speed of 80 km/h from town X to town Y, located 800 km from each other. At the same moment that the train departed, a passenger started to walk back and forth from one end of car B to the other at a speed of 100 cm/s. Arriving in town Y, the passenger had already gone and returned 720 times. The length of car A is that of car B plus one fourth of the length of the locomotive, and the length of the locomotive equals the length of car A plus one fifth of the length of car B. What is the total length of the train?Level VI20) Several faucets were used to fill up six tanks. For one hour, all the faucets discharged water in a reservoir, which distributed it between four of these tanks: A, B, C and D. After that, for one hour, the faucets discharged water in a double funnel which directed half of the water to tanks E and F and the other half to the reservoir which, in turn, continued to distribute its water between tanks A, B, C and D. With this, tanks A, B, C and D were full. To fill tanks E and F up, it was necessary to use one faucet, which, for two hours, distributed its water between tanks E and F. After this all the six tanks were full. What was the number of faucets initially used? (Note: all the faucets had the same water flow rate and all the tanks had the same volume).21) Several rectangles are drawn on a plane surface in such a way that their intersecting lines form 18,769 areas not further subdivided. What is the minimum number of rectangles that must be drawn to form the described pattern?22) Several straight line segments are drawn on a plane surface in such a way that their intersecting lines form 1,597 areas that are not further subdivided. What is the minimum number of line segments that must be drawn to form the described pattern?23) 1 + 10^1,234,567,890 triangles are drawn on a plane surface. What is the maximum number of areas, not further subdivided, that can be formed as these triangles intersect each other? (Contributed by Rodrigo de Almeida Rodrigues)24) According to Fermat’s Last Theorem, a^n + b^n = c^n has no solutions for n > 2 (a, b, c andn must be positive integers). In 1992, I proved this in a simple, yet incorrect manner. This was my reasoning: Fermat’s Theorem is a generalization of Pythagoras’ Theorem, which asserts that the sum of areas of the squares drawn on the legs (short sides) of a right triangle equals the area of a square drawn on the hypotenuse of the same right triangle (a^2 + b^2 = c^2). If we try to generalize that theorem, going from 2 to 3 dimensions (a^3 + b^3 = c^3), we have a triangular prism formed by displacement of a right triangle along an axis perpendicular to its face, as illustrated by the figure below.We can construct a cube on one of the three quadrangular faces of that prism. Two of those faces correspond to the legs of the right triangle (ADFB, BFEC) while the larger face corresponds to the hypotenuse (ADEC). It is possible to construct a cube on one of the faces, implying that the 4 sides of that face have the same length. This affects the whole prism, causing the cube constructed on the other face to have the same size than that constructed on the first, for if AB=BF and BF=BC, then AB=BC. In that way, no cube can be constructed on the third face, for if AC represents the hypotenuse, then AC cannot be equal to to AB. Therefore, a^n + b^n = c^n has no solution for n=3. Following the same line of reasoning, we can show that it has no solution for any number of dimensions larger than 2. What is the error in this proof?Level VII25) A certain gear system consists of 5 concentric, superposed discs: A, B, C, D and E, which are mounted on a solid platform, taken as a stationary reference. The discs have different sizes and spin at different speeds. All the discs spin at constant rates, some clockwise, some anticlockwise. Each disc has a red dot on its surface, and initially all these red dots are not lined up. At a given moment, all the discs start to spin simultaneously, each at its own speed, without any contact between them. It takes 7 minutes for disc A, 13 minutes for disc B, 17 minutes for disc C, 19 minutes for disc D and 23 minutes for disc E to complete a full 360-degree spin. After a certain time, all the red dots were aligned, disc A being in the same position that it was 2 minutes after the discs started to spin, disc B being in the same position that it was 3 minutes after the discs started to spin, disc C being in the same position that it was 4 minutes after the discs started to spin, disc D being in the same position that it was 7 minutes after the discs started to spin, and disc E being the same position that it was 9 minutes after the discs started to spin. How much time elapsed from the moment the discs started to spin until the discs reached that configuration for the first time?26) Pedrinho entered Dona Maria’s Stationer´s Shop and asked her to sell him a geometric ruler for drawing a spiral with a small concentric circle. Dona Maria, a Sigma Society member, told the boy that there were no rulers for drawing spirals. But after thinking the problem over, she found a way to make a drawing like that, and described the method to the boy. She sold the boy the material needed right away, which he paid with a US$ 10.00 note, receiving some change. He went home and made the drawing without any problems. Describe a method to perform Pedrinho’s task having the same US$ 10.00 at your disposal for buying the material needed. The drawing must show a satisfactory agreement with the described pattern (a spiral with a small concentric circle), without large irregularities in the spiral. (Modified in 31 Aug 2001 at the suggestion of our friends Petri Widsten and Nikos Lygeros, as the earlier question with the 9 cubes was similar to one of the questions of the Eureka Test).27) A man takes a deep breath, filling his lungs completely with air. Then he holds his breath and a tape measure is used to measure his chest circumference, which turns out to be 106 cm. After that, the man exhales so that all the air is expelled from his lungs. His chest circumference is measured again, and is now 84 cm. Having $10 at your disposal for buying material, find out the volume of air that his lungs are able to hold.28) The speed of a person’s reflexes can be determined based on the time elapsed between a stimulus and the response of that stimulus. For example: A lamp remains unlit while we observe it. On receiving the stimulus “the lamp was lit”, the reaction is to be “close the eyes”. The shorter the time between “the lamp was lit” and “close the eyes”, the faster the reflexes. Describe a method to determine the speed of a person’s reflexes, without using a chronometer or any other equipment allowing the measurement of time intervals shorter than 1 second. It is possible to devise a rough method on a US$ 1 budjet for equipment, and a sophisticated method with good precision having US$ 1,000 at one’s disposal. Describe a method for both budjets.29) In 1993, in an essay about Science and Religion, I described a project regarding the possibility to build an “invisibility machine”. On describing the details, I realized that some problems were insolvable, not only because of technological limitations but also for physical reasons imposing theoretical and possibly insurmountable limits. The project starts from the central idea that in order to make an object invisible, it is necessary for an external observer looking in its direction to visually stop noticing its presence. This can be done in the following way: A sphere is constructed, and its whole external surface is covered with minute, high-resolution TV cameras and monitors. Millions or even billions of cameras and monitors are to cover the whole sphere in such a way that each monitor transmits the image captured by a camera located in the point diametrically opposite to that monitor. The result will be as shown in the figure below.The image of the object (blue square) is captured by a camera located in point A, which transmits the image to a monitor in point M. As a result, an observer in point O will see the blue square as if there were nothing in front of him. In that way, everything inside the sphere will be invisible to the external observer. But this scheme presents two problems. One of them can be solved in theory while the other one is insolvable. Indicate those two problems and explain why one of them can be solved but the other one cannot.Level VIII30) The porous and gray “lead” inside a pencil consists of a mixture of graphite and clay. The ratio of graphite to clay is not known. On writing on a sheet of paper, a fine layer of “lead” remains on the surface of the sheet. Describe a method for calculating the mass of “lead” in the dot of the letter “i”. You may use only US$10 to buy the material needed for the experiment.31) We have a cylinder with a radius of 50 cm and a tape measure 0.01 cm thick. The height of the cylinder equals the width of the tape measure. The thickness of the tape measure is invariable and one of its wider sides is inextensible. What is the minimum length of tape necessary to wind it around the cylinder 9 times, all rounds overlapping, as in a roll of scotch tape. The top and base of the cylinder may not be covered with tape. The solution must be given with 14 significative digits and it is not allowed to cut the tape or cut or deform de cylinder.32) A sophisticated aircraft is hovering like a hummingbird over a terrain located on the equatorial line of a planet, at an altitude of 1,000 m. The planet is completely spherical and homogeneous, and has a small satellite on a circular orbit on a plane parallel to its equator. At 15:58:30h a man parachutes down from the aircraft, descending perpendicularly to the ground. At the moment that he jumps off the aircraft, he notices a satellite starting to rise on the eastern horizon. He lands and, without leaving the landing site, continues to observe the satellite, which at 17:40:00 h reaches the zenith. He remains in the same place, observing…and at 19:20:00h sees the satellite disappear on the western horizon. Still in the same place, at 22:40:00h, he sees the satellite rising again in the east. What is the approximate diameter of that planet? Explain how you arrived at your answer and the usefulness of all the pieces of information given. Explain also why the result cannot be exact.(If you have doubts as to the meaning of zenith, horizon, equator, orbit etc., you may consult dictionaries or encyclopaedias).Level IX33) Describe a practical and fast method that can be used with good precision to determine the number of words in a person’s vocabulary.34) There was a brillant anthropologists, member of Sigma V, named João. During an expedition to Africa he was captured by a tribe of cannibals and sentenced to serve as a meal. However, the “legislation” of the tribe offered the prisoners a chance to be freed should they be able to overcome a challenge. In the case of João, the challenge was as follows: he would be presented with two chicken eggs, one of them raw and the other one boiled. There would be two boxes. The raw egg would be placed in one box and the boiled egg in the other one. João doesn’t know what the dimensions of the boxes are until he faces the challenge. The walls of the boxes are rigid and opaque. The have the shape of a parallelepiped. One of the boxes has a window in one of its walls. The window is covered by a wire screen whose mesh size João does not know until he faces the challenge. Through the window it it is possible to observe the egg inside the box.The challenge is to find out within 2 minutes which one of the two eggs is raw. It is not allowed to break the eggs, take the eggs out of the boxes or open the boxes. Nothing solid, liquid or gaseous may be put inside the boxes.João is informed that the challenge would be presented to him after 90 days. Before that, he may count on the help of the villagers to help him work out a solution to the problem. Aside from that, he has the use of all “sophisticated” instruments and everything else that he can find in the village and its surroundings. When the time came for him to face the challenge, at dawn, João was blindfolded and his hands were tied. A few minutes after that, an old villager took an egg, boiled it, dried it, and placed it in a box which he closed. He then took a raw egg and put it in another box, closing the box immediately. The two boxes were placed on a table where they stayed until nightfall. Then João’s hands were untied, the blindfold was removed, he was supplied with the equipment he had requested earlier, and he was taken to the table on which the boxes containing the eggs were lying. He examined them carefully and succeeded in finding out which box contained the raw egg. The challenge was repeated daily for a period of 20 days, each time with different eggs, and every time he was able to identify the raw egg. The admiring cannibals then proceeded to set him free and even gave him lots of jewelry as a gift. How did João manage to save himself?We are recommending those who are taking the "Sigma " test ,not to try out the quest in real life !It can bring you into very dangerous situation.We don't take any kind of responsibility for possible physical or other problems caused by trying out the questions in real life.We would like to tell you about the following true story, which has made a deep impression on us, the story tells what might happen if you try to carry out the questions in reality.35) An Arab man and an Israeli woman are abducted by extraterrestrials. The E.T.s promise to return them to Earth unharmed, provided that they succeed in the following task: three rooms are designated A, B and C. Each room is square and measures approximately 25 m2. The rooms are connected in such a way that each room has two doors, and each door provides access to one of the other two rooms. The three rooms are acustically isolated and have no furniture or windows. The walls, doors, ceiling and floor of the rooms are solid and opaque, and contain no cracks, holes, hidden passages or the like. The man is placed in room A and the woman in room B. They both receive the following instructions:1- They both have 1 hour to traverse the three rooms and return to the room where they started, always walking in the direction A - B - C - A.2- The both have to remain seated, on the floor, in their respective rooms, until a signal would be emitted, indicating that the time count had started. The signal was as follows: on each door there are two lamps (one on each side of the door), and the nearly simultaneous lighting of the all the lamps constitutes the signal. Each lamp is bright enough for a person to notice easily even when he is not paying attention to it.3- The moment that the woman touches the doorknob of a room, the man cannot be in that room any more.4- The moment that the man touches the doorknob of a room, the woman cannot be in that room any more.5- The woman has to get up from the floor after the man.6- The man and woman are not permitted to communicate between each other in any way, or obtain from others any information allowing them to figure out where the other one is. They may not beat the walls or the doors, or try to generate any kind of shock wave. On leaving a room and entering another one, it is required to close the corresponding door. Initially all the doors are closed. Two or more doors may not be open at the same time.7- None of them has a clock or any other instrument that can be used to measure time.8- 1 minute before the 1 hour period is up the light signal will be given again, indicating that the time is running out.9- When the 1 hour period is up the man has to be sitting in the center of room A and the woman in the center of room B.10- The woman may only sit down after the man.11- The man is told that the woman is exceptionally intelligent.12- The woman is told that the man is exceptionally intelligent.The man and the woman did not know each other and had never been in any contact with each other before. They did not communicate with each other during the whole process (to clarify the matter, it can be told that they both were mute and deaf). The experiment is carried out and they manage to perform the task. The experiment is repeated 10 times and each time they complete the task successfully, making it clear that the first time was not due to mere good luck. Afterwards they are returned to Earth where they convert to Zoroastrianism, get married and live happily everafter! Describe the method they used and the way of thinking of both of them.Level X - EXTRA (it is required to get at least 3 questions of levels VII-IX right to try to answer this question)36) The great poet Joao spent the last days of his life lodged in the cellar of his friend Jose·s house. Jose, a petty merchant, was a man with meager possessions but very generous. Before dying, Joao entrusted his friend with an unpublished poem. The title of the poem, published posthumously, is irrelevant to the problem at hand.Joao called that humble and generous friend just ·Amphibian·. Once his friend asked him why he always called him by that name, and Joao explained.Take into consideration that Joao held his friend in high esteem and, within the context, find a logical explanation for the meaning of ·Amphibian·.[This text is based on real-life events]© 2018 von Goethe IV

How do you measure the IQ of someone who finds regular IQ tests boring and or annoying and has no interest in taking them in particular?You don’t bother.I am semi-professional in the IQ ‘Industry’ and in my experience the ‘brightest’ of people often love the challenge of testing their intellectual ability. The Test below, is generally considered to be rather fascinating.Try this Test, below:You may use reference books to assist you. You may take as long as you wish. I have completed this test - (send your answer sheet to me and I will mark it free of charge - contact me through Quora):TESTLevel I1) In 1976 Marcelo was 11 years old. How old will he be in 1999?2) If 13 bullets cost $3.90, how much do 31 bullets cost?3) A box measures 60 cm x 50 cm x 30 cm. What is the maximum number of smaller boxes measuring 10 cm x 10 cm x 10 cm that fit in it?4) 12 people do a job in 12 days. How many people are needed to do the same job in 1 day?5) A collection consists of 12 volumes. There are 300 pages in each volume, 50 lines on each page, and 100 letters on each line. What is the total number of letters in the collection?Level II6) A company has enough stock to supply its clientele of 2,500 people for 12 months. How long would this stock last if the clientele grew to 6,000 people?7) If one horse can pull 600 kg, how many horses are needed to pull 6,150 kg?8) Fernanda’s and Andreia’s ages total 18 years. What are their individual ages, given that Andreia is twice as old as Fernanda?Level III9) Ricardo weighs 30% more than José. If Ricardo were to lose 10% and José gain 20% of weight, which one of them would weigh more after that. Explain.10) A planetary system has, in addition to the main star, 9 planets. Each planet has 7 primary satellites. One out of every 21 primary satellites has 3 co-orbital satellites. How many celestial bodies are there all together?11) On a staircase with 1,000 steps there was 1 gram of gold on the 1st step, 2 grams on the 2nd, 3 grams on the 3rd, 4 grams on the 4th, 5 grams on the 5th and so on, so that there was 1 kg of gold on the last step. Given that 1 gram of gold is worth 11 dollars, calculate the total value of the gold on the staircase (in dollars).Level IV12) 99% of the people in a room are men. How many men would have to leave the room in order for this percentage to decrease to 98%? It is known that the number of women in the room is 3.13) On a chessboard with 64 squares (8 x 8), two kings can occupy 3,612 different positions. How many different positions can two kings occupy on a chessboard with 117 squares (13 x 9). Two kings may not be on the same square at the same time or occupy adjacent squares.14) Marcelo had apples, half of which he gave to his brother. The latter gave 75% of the apples that he had gotten to be equally shared between his three cousins: Anderson, João and Mané. Anderson bought 7 apples more and gave half of all his apples to his brother Mané. Mané’s apples then totaled 17. How many apples did João get?15) Maria went to a farm to buy eggs. Returning home, she gave half of them to her sister who, in turn, gave a third of those she had gotten to her boyfriend. The latter, after eating one third of the eggs that he had gotten, gave the rest to his cousin. Given that each egg weighs 70 grams, that Maria cannot carry more than 2.5 kg, and that the eggs were raw, calculate how many eggs the cousin of Maria’s sister’s boyfriend received.16) The mayor João and an important bachelor businessman, called José, held a large barbecue. Aside from the businessman José, the mayor João and his wife, the number of people present equaled the number of 100 dollar notes that the mayor spent multiplied by the the number of 100 dollar notes that the businessman spent. Given that, on average, every person consumed the equivalent of US$6.40 and that the mayor invested US$1,700, calculate how much the businessman José invested. (Note: the businessman José, the mayor João and his wife took part in the consumption)Level V17) A Formula-1 race car is racing around a circular track, completing the first lap in 3 minutes with an average speed of 144 km/h. In what time must a second lap be driven in order for the average speed of the two laps to increase to 300 km/h?18) When Antônio looked at his watch, he noticed that the hour hand was lying exactly over the minute hand. What time will it take for this to happen again? (both hands move at constant rates)19) A train with 2 cars is traveling at a speed of 80 km/h from town X to town Y, located 800 km from each other. At the same moment that the train departed, a passenger started to walk back and forth from one end of car B to the other at a speed of 100 cm/s. Arriving in town Y, the passenger had already gone and returned 720 times. The length of car A is that of car B plus one fourth of the length of the locomotive, and the length of the locomotive equals the length of car A plus one fifth of the length of car B. What is the total length of the train?Level VI20) Several faucets were used to fill up six tanks. For one hour, all the faucets discharged water in a reservoir, which distributed it between four of these tanks: A, B, C and D. After that, for one hour, the faucets discharged water in a double funnel which directed half of the water to tanks E and F and the other half to the reservoir which, in turn, continued to distribute its water between tanks A, B, C and D. With this, tanks A, B, C and D were full. To fill tanks E and F up, it was necessary to use one faucet, which, for two hours, distributed its water between tanks E and F. After this all the six tanks were full. What was the number of faucets initially used? (Note: all the faucets had the same water flow rate and all the tanks had the same volume).21) Several rectangles are drawn on a plane surface in such a way that their intersecting lines form 18,769 areas not further subdivided. What is the minimum number of rectangles that must be drawn to form the described pattern?22) Several straight line segments are drawn on a plane surface in such a way that their intersecting lines form 1,597 areas that are not further subdivided. What is the minimum number of line segments that must be drawn to form the described pattern?23) 1 + 10^1,234,567,890 triangles are drawn on a plane surface. What is the maximum number of areas, not further subdivided, that can be formed as these triangles intersect each other? (Contributed by Rodrigo de Almeida Rodrigues)24) According to Fermat’s Last Theorem, a^n + b^n = c^n has no solutions for n > 2 (a, b, c andn must be positive integers). In 1992, I proved this in a simple, yet incorrect manner. This was my reasoning: Fermat’s Theorem is a generalization of Pythagoras’ Theorem, which asserts that the sum of areas of the squares drawn on the legs (short sides) of a right triangle equals the area of a square drawn on the hypotenuse of the same right triangle (a^2 + b^2 = c^2). If we try to generalize that theorem, going from 2 to 3 dimensions (a^3 + b^3 = c^3), we have a triangular prism formed by displacement of a right triangle along an axis perpendicular to its face, as illustrated by the figure below.We can construct a cube on one of the three quadrangular faces of that prism. Two of those faces correspond to the legs of the right triangle (ADFB, BFEC) while the larger face corresponds to the hypotenuse (ADEC). It is possible to construct a cube on one of the faces, implying that the 4 sides of that face have the same length. This affects the whole prism, causing the cube constructed on the other face to have the same size than that constructed on the first, for if AB=BF and BF=BC, then AB=BC. In that way, no cube can be constructed on the third face, for if AC represents the hypotenuse, then AC cannot be equal to to AB. Therefore, a^n + b^n = c^n has no solution for n=3. Following the same line of reasoning, we can show that it has no solution for any number of dimensions larger than 2. What is the error in this proof?Level VII25) A certain gear system consists of 5 concentric, superposed discs: A, B, C, D and E, which are mounted on a solid platform, taken as a stationary reference. The discs have different sizes and spin at different speeds. All the discs spin at constant rates, some clockwise, some anticlockwise. Each disc has a red dot on its surface, and initially all these red dots are not lined up. At a given moment, all the discs start to spin simultaneously, each at its own speed, without any contact between them. It takes 7 minutes for disc A, 13 minutes for disc B, 17 minutes for disc C, 19 minutes for disc D and 23 minutes for disc E to complete a full 360-degree spin. After a certain time, all the red dots were aligned, disc A being in the same position that it was 2 minutes after the discs started to spin, disc B being in the same position that it was 3 minutes after the discs started to spin, disc C being in the same position that it was 4 minutes after the discs started to spin, disc D being in the same position that it was 7 minutes after the discs started to spin, and disc E being the same position that it was 9 minutes after the discs started to spin. How much time elapsed from the moment the discs started to spin until the discs reached that configuration for the first time?26) Pedrinho entered Dona Maria’s Stationer´s Shop and asked her to sell him a geometric ruler for drawing a spiral with a small concentric circle. Dona Maria, a Sigma Society member, told the boy that there were no rulers for drawing spirals. But after thinking the problem over, she found a way to make a drawing like that, and described the method to the boy. She sold the boy the material needed right away, which he paid with a US$ 10.00 note, receiving some change. He went home and made the drawing without any problems. Describe a method to perform Pedrinho’s task having the same US$ 10.00 at your disposal for buying the material needed. The drawing must show a satisfactory agreement with the described pattern (a spiral with a small concentric circle), without large irregularities in the spiral. (Modified in 31 Aug 2001 at the suggestion of our friends Petri Widsten and Nikos Lygeros, as the earlier question with the 9 cubes was similar to one of the questions of the Eureka Test).27) A man takes a deep breath, filling his lungs completely with air. Then he holds his breath and a tape measure is used to measure his chest circumference, which turns out to be 106 cm. After that, the man exhales so that all the air is expelled from his lungs. His chest circumference is measured again, and is now 84 cm. Having $10 at your disposal for buying material, find out the volume of air that his lungs are able to hold.28) The speed of a person’s reflexes can be determined based on the time elapsed between a stimulus and the response of that stimulus. For example: A lamp remains unlit while we observe it. On receiving the stimulus “the lamp was lit”, the reaction is to be “close the eyes”. The shorter the time between “the lamp was lit” and “close the eyes”, the faster the reflexes. Describe a method to determine the speed of a person’s reflexes, without using a chronometer or any other equipment allowing the measurement of time intervals shorter than 1 second. It is possible to devise a rough method on a US$ 1 budget for equipment, and a sophisticated method with good precision having US$ 1,000 at one’s disposal. Describe a method for both budgets.29) In 1993, in an essay about Science and Religion, I described a project regarding the possibility to build an “invisibility machine”. On describing the details, I realized that some problems were insolvable, not only because of technological limitations but also for physical reasons imposing theoretical and possibly insurmountable limits. The project starts from the central idea that in order to make an object invisible, it is necessary for an external observer looking in its direction to visually stop noticing its presence. This can be done in the following way: A sphere is constructed, and its whole external surface is covered with minute, high-resolution TV cameras and monitors. Millions or even billions of cameras and monitors are to cover the whole sphere in such a way that each monitor transmits the image captured by a camera located in the point diametrically opposite to that monitor. The result will be as shown in the figure below.The image of the object (blue square) is captured by a camera located in point A, which transmits the image to a monitor in point M. As a result, an observer in point O will see the blue square as if there were nothing in front of him. In that way, everything inside the sphere will be invisible to the external observer. But this scheme presents two problems. One of them can be solved in theory while the other one is insolvable. Indicate those two problems and explain why one of them can be solved but the other one cannot.Level VIII30) The porous and gray “lead” inside a pencil consists of a mixture of graphite and clay. The ratio of graphite to clay is not known. On writing on a sheet of paper, a fine layer of “lead” remains on the surface of the sheet. Describe a method for calculating the mass of “lead” in the dot of the letter “i”. You may use only US$10 to buy the material needed for the experiment.31) We have a cylinder with a radius of 50 cm and a tape measure 0.01 cm thick. The height of the cylinder equals the width of the tape measure. The thickness of the tape measure is invariable and one of its wider sides is inextensible. What is the minimum length of tape necessary to wind it around the cylinder 9 times, all rounds overlapping, as in a roll of scotch tape. The top and base of the cylinder may not be covered with tape. The solution must be given with 14 significant digits and it is not allowed to cut the tape or cut or deform the cylinder.32) A sophisticated aircraft is hovering like a hummingbird over a terrain located on the equatorial line of a planet, at an altitude of 1,000 m. The planet is completely spherical and homogeneous, and has a small satellite on a circular orbit on a plane parallel to its equator. At 15:58:30h a man parachutes down from the aircraft, descending perpendicularly to the ground. At the moment that he jumps off the aircraft, he notices a satellite starting to rise on the eastern horizon. He lands and, without leaving the landing site, continues to observe the satellite, which at 17:40:00 h reaches the zenith. He remains in the same place, observing…and at 19:20:00h sees the satellite disappear on the western horizon. Still in the same place, at 22:40:00h, he sees the satellite rising again in the east. What is the approximate diameter of that planet? Explain how you arrived at your answer and the usefulness of all the pieces of information given. Explain also why the result cannot be exact.(If you have doubts as to the meaning of zenith, horizon, equator, orbit etc., you may consult dictionaries or encyclopedias).Level IX33) Describe a practical and fast method that can be used with good precision to determine the number of words in a person’s vocabulary.34) There was a brillant anthropologists, member of Sigma V, named João. During an expedition to Africa he was captured by a tribe of cannibals and sentenced to serve as a meal. However, the “legislation” of the tribe offered the prisoners a chance to be freed should they be able to overcome a challenge. In the case of João, the challenge was as follows: he would be presented with two chicken eggs, one of them raw and the other one boiled. There would be two boxes. The raw egg would be placed in one box and the boiled egg in the other one. João doesn’t know what the dimensions of the boxes are until he faces the challenge. The walls of the boxes are rigid and opaque. The have the shape of a parallelepiped. One of the boxes has a window in one of its walls. The window is covered by a wire screen whose mesh size João does not know until he faces the challenge. Through the window it it is possible to observe the egg inside the box.The challenge is to find out within 2 minutes which one of the two eggs is raw. It is not allowed to break the eggs, take the eggs out of the boxes or open the boxes. Nothing solid, liquid or gaseous may be put inside the boxes.João is informed that the challenge would be presented to him after 90 days. Before that, he may count on the help of the villagers to help him work out a solution to the problem. Aside from that, he has the use of all “sophisticated” instruments and everything else that he can find in the village and its surroundings. When the time came for him to face the challenge, at dawn, João was blindfolded and his hands were tied. A few minutes after that, an old villager took an egg, boiled it, dried it, and placed it in a box which he closed. He then took a raw egg and put it in another box, closing the box immediately. The two boxes were placed on a table where they stayed until nightfall. Then João’s hands were untied, the blindfold was removed, he was supplied with the equipment he had requested earlier, and he was taken to the table on which the boxes containing the eggs were lying. He examined them carefully and succeeded in finding out which box contained the raw egg. The challenge was repeated daily for a period of 20 days, each time with different eggs, and every time he was able to identify the raw egg. The admiring cannibals then proceeded to set him free and even gave him lots of jewelry as a gift. How did João manage to save himself?35) An Arab man and an Israeli woman are abducted by extraterrestrials. The E.T.s promise to return them to Earth unharmed, provided that they succeed in the following task: three rooms are designated A, B and C. Each room is square and measures approximately 25 m2. The rooms are connected in such a way that each room has two doors, and each door provides access to one of the other two rooms. The three rooms are acustically isolated and have no furniture or windows. The walls, doors, ceiling and floor of the rooms are solid and opaque, and contain no cracks, holes, hidden passages or the like. The man is placed in room A and the woman in room B. They both receive the following instructions:1- They both have 1 hour to traverse the three rooms and return to the room where they started, always walking in the direction A - B - C - A.2- The both have to remain seated, on the floor, in their respective rooms, until a signal would be emitted, indicating that the time count had started. The signal was as follows: on each door there are two lamps (one on each side of the door), and the nearly simultaneous lighting of the all the lamps constitutes the signal. Each lamp is bright enough for a person to notice easily even when he is not paying attention to it.3- The moment that the woman touches the doorknob of a room, the man cannot be in that room any more.4- The moment that the man touches the doorknob of a room, the woman cannot be in that room any more.5- The woman has to get up from the floor after the man.6- The man and woman are not permitted to communicate between each other in any way, or obtain from others any information allowing them to figure out where the other one is. They may not beat the walls or the doors, or try to generate any kind of shock wave. On leaving a room and entering another one, it is required to close the corresponding door. Initially all the doors are closed. Two or more doors may not be open at the same time.7- None of them has a clock or any other instrument that can be used to measure time.8- 1 minute before the 1 hour period is up the light signal will be given again, indicating that the time is running out.9- When the 1 hour period is up the man has to be sitting in the center of room A and the woman in the center of room B.10- The woman may only sit down after the man.11- The man is told that the woman is exceptionally intelligent.12- The woman is told that the man is exceptionally intelligent.The man and the woman did not know each other and had never been in any contact with each other before. They did not communicate with each other during the whole process (to clarify the matter, it can be told that they both were mute and deaf). The experiment is carried out and they manage to perform the task. The experiment is repeated 10 times and each time they complete the task successfully, making it clear that the first time was not due to mere good luck. Afterwards they are returned to Earth where they convert to Zoroastrianism, get married and live happily ever after! Describe the method they used and the way of thinking of both of them.Level X - EXTRA (it is required to get at least 3 questions of levels VII-IX right to try to answer this question)36) The great poet Joao spent the last days of his life lodged in the cellar of his friend Jose·s house. Jose, a petty merchant, was a man with meager possessions but very generous. Before dying, Joao entrusted his friend with an unpublished poem. The title of the poem, published posthumously, is irrelevant to the problem at hand.Joao called that humble and generous friend just ·Amphibian·. Once his friend asked him why he always called him by that name, and Joao explained.Take into consideration that Joao held his friend in high esteem and, within the context, find a logical explanation for the meaning of ·Amphibian·.[This text portion is based on real-life events]© 2018 von Goethe IV (Ubermensch I)