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Wow, this post is long!Here is the tl,dr; version:We start with the 21 candidates.We show a simple lemma that can give us some lower bound for the number of questions we need.We design a simple recursive algorithm to check all possible ways of asking the questions. We use the above lemma to prune almost all branches of the search.Within the simple algorithm, we use a solver of linear programs to check whether an answer is still feasible.The smallest number of questions is indeed 6.Jaimal Ichharam explains nicely how we can reduce the number of possible answers to 21. In fact, it is impossible to reduce it any further: for each of those 21 options it is possible to construct a set of 8 weights such that it is the (only) answer.Now, the number 21 can be used to prove that we need at least 4 questions in the worst case. This is not an optimal lower bound (as we shall see later), but the proof is very simple. The argument is the same information-theoretic one that can be used to prove that searching in a sorted array is [math]\Omega(\log n)[/math] and that comparison-based sort is [math]\Omega(n\log n)[/math]: in order to distinguish among many possibilities, you need enough information, and for that you need to ask enough questions.Lemma: Any deterministic algorithm that solves the "8 bags problem" and always makes at most [math]q[/math] questions can distinguish between at most [math]2^{q+1}-1[/math] different candidates.Proof: The number is the maximal number of different outputs our program can produce. And if there are more candidates than possible outputs, some candidate is never output, and therefore the program cannot be correct.Why is that the maximum number of possible outputs? We'll prove that by using induction. If [math]q=1[/math], we get to ask 1 question, and then we can give 3 different answers: one in the case the left side of the scale was lighter, one if it was heavier, and one if they were equal. (In the last case, the answer would be that this is the split we are looking for.)In the general case with [math]q[/math] questions, after the program asks the first question, there are three branches. If the two pans were equal we know the answer and terminate. In each of the other two cases we have [math]q-1[/math] questions left and thus (by the induction hypothesis) we can give at most [math]2^q - 1[/math] different outputs. Thus the total number of different outputs for a program that asks [math]q[/math] questions is at most [math]1+2(2^q-1)[/math], q.e.d.(Note that a very similar lemma can be used in any other problem where our questions can receive the answers <, =, >, and where getting the answer = uniquely determines the correct answer. Do you see the similarity to binary search?)Corollary: If we ask at most 3 questions, we can have at most 15 different outputs. Therefore we need at least 4 questions to distinguish among 21 candidates.Even though the lemma does not give a tight lower bound, it is still important: we will use it later to prune our search.Our ultimate goal will be to implement a brute force search that will consider all orders in which we can ask the questions. The schema of the algorithm is very simple:is_solvable(number_of_questions, past):  count the answers that are consistent with the past  if there is at most one, return True  if we are down to 0 questions left, return False  for each possible answer A:  p1 = past + [ when weighing A left pan is lighter ]  p2 = past + [ when weighing A left pan is heavier ]  if is_solvable(number_of_questions-1, p1)  and is_solvable(number_of_questions-1, p2): return True  return False That is it. In each possible situations, consider all possible (meaningful) questions you could ask next. The current situation is solvable in [math]q[/math] questions if and only if you can now ask a question such that regardless of the answer you get you can guarantee solving the new state in [math]q-1[/math] questions.One additional optimization of this algorithm is our use of the above lemma. Instead of "if we are down to 0 questions left (and have more than 1 candidate), return False" we can have the more general check "if the number of candidates is too large for the number of questions, return False".The only "building block" we now need is the check whether a given candidate is consistent with a given set of answers we already have. So let's take a look at that.What do we have at the beginning? Eight unknown weights: [math]0\leq w_1<w_2<\cdots<w_8[/math]. Now, each time we ask a question and don't find the correct split, we get a new information of the following form:[math][/math][math] w_1 [/math][math][/math][math]+ w_3 [/math][math][/math][math]+ w_4 [/math][math][/math][math]+ w_8 < w_2 [/math][math][/math][math]+ w_5 [/math][math][/math][math]+ w_6 [/math][math][/math][math]+ w_7[/math]Now, what does it mean when we say that an answer is still feasible? It means that the above system of inequalities is consistent with equality in that particular case.(Technical note: To be completely correct, our check for feasibility should find such values of weights that not only is there equality in our case, but at the same time there must be inequalities in all other cases. However, this is trivially true: whenever we have weights such that more than one split would balance the scales, we can apply some small random perturbation to the weights so that there would only be equality in the one case we want. Details are left as an exercise.)In order to do the above checks I use an LP solver (lp_solve in particular). Checking whether a system of inequalities and equalities has a solution is pretty close to linear programming. The only technicality we need to deal with are the sharp inequalities. Luckily, in our case we can simply turn them into less-than-or-equal inequalities by simply requiring the difference to be at least 1. (Note that the weights can always be scaled.)Here is a sample linear program:min: w8; w1+1 <= w2; w2+1 <= w3; w3+1 <= w4; w4+1 <= w5;  w5+1 <= w6; w6+1 <= w7; w7+1 <= w8; w1+w3+w6+w8+1 <= w2+w4+w5+w7; w1+w2+w3+w8+1 <= w4+w5+w6+w7; w1+w2+w4+w8 = w3+w5+w6+w7; Without the last constraint this program is feasible. One possible assignment of weights is (0,2,3,4,5,6,7,8). With the last constraint the program stops being feasible, so the corresponding way of splitting the bags cannot be the solution any more after those two weighings.(Note that I chose minimizing the maximum weight as the goal of the LP. This is pretty much arbitrary, any positive linear combination of our variables would do, as we are only interested in the existence of a solution.)Code posted here: http://ideone.com/xnivHM(Runs for about 3 minutes on my laptop, verifies that there is no solution with fewer than 6 questions in the worst case, and finds one with 6. Keeping the past in sorted order and adding memoization brings runtime down under a minute.)Some simple modifications of the code above can give us an optimal strategy as well. Here's one that I found by making some arbitrary choices:The first three questions will always be the same: 1567 vs. 2348, 1458 vs. 2367, and 1368 vs. 2457. If one of them is the solution, we are done. Otherwise, we get one of 8 possible combinations of < and >. Each of them will correspond to at most 7 candidates. These are the feasible answers at this point:<<<: 1468 1568 1278 1378 1478 1578 1678  <<>: 1268 1278  <><: 1278 1378  <>>: 1238 1248 1348 1258 1358 1268 1278  ><<: 1467 1468 1278 1378 1478  ><>: 1267 1367 1467 1268 1278  >><: 1456 1457 1467 1278 1378  >>>: 1467 1258 1358 1268 1278  If 1368 < 2457, compare 1378 vs. 2456 as the fourth question, otherwise compare 1268 vs. 3457 as the fourth question. In most cases you'll be left with at most 3 feasible solutions, and that is trivial to solve in two questions. There are only two cases that are harder:: <<<<: 1468 1568 1478 1578 1678 <>>>: 1238 1248 1348 1258 1358 Both of these can again be solved in two questions, an optimal strategy is left as an exercise.

Hey, this is a very broad question, do you mean which Tecno brands are most popular or which other phone brands are popular? I am going to answer the former based on my country of residence, Uganda as a sample space since am in Africa.Yes, Tecno is a popular brand in Africa and it has continued to grow with more people buying their products in the recent 4 years.To answer your question, based on my current analysis and since I myself work with an online store (Innovware). The most common and popular Tecno brands so far based on current trends include the following;Tecno Boom J8Tecno Phantom 5 to 6Tecno Camon CX and CX Air modelsTecno L8 modelsTecno SparkTecno W3, W4 and W5 modelsTecno along the way has discountinued several of its brand lines which makes it impossible to find another once they're out of stock. However, the Tecno Boom J8 is one of the few brands which have been maintained and many consumers have continued to buy it due to its popularity.Other popular brands are: Samsung, Huawei, LG, Itel, Infinix, Nokia, HTC, iPhone.I hope my answer meets your needs.

Following are the various methods available for the determination of water content of soil:1. Oven-Drying Method2. Sand Bath Method3. Alcohol Method4. Infrared Lamp Torsion Balance Method5. Calcium Carbide Method6. Pycnometer Method.1. Oven-Drying Method:The oven-drying method is the standard method of the determination of water content in the laboratory.Principle:The principle of test is to determine the weight of a wet soil sample in a container, dry the sample along with the container for 24 h in an oven and then determine the weight of the dry soil sample. The sequence of steps in water content determination is illustrated in Fig. 4.8.The water content of the soil (ω, in percentage) is obtained from the relation –ω = [(W2 – W1)/(W3 – W1)] x 100 …(4.66)where,W1 is the weight of the container,W2 is the weight of container + wet soil, andW3 is the weight of container + dry soil.Procedure:Water content of a soil sample is determined in the following steps:i. A clean dry non-corrodible container with lid is taken and its weight is determined (W1) using a balance. The balance should be of minimum sensitivity to weigh the samples to an accuracy of 0.04% of weight of soil taken. This comes to a sensitivity of 0.01 g.ii. The required quantity of a representative undisturbed soil sample, is taken and placed loosely in the container. The weight of the container with lid and wet soil is determined (W2).iii. The container with wet soil is placed in the oven with its lid removed for 24 h, maintaining a temper­ature of 110 ± 5°C. The container now containing dry soil is then cooled in a desiccator with the lid closed.iv. The weight of dry soil with the container and lid (W3) is determined. The water content is determined from Eq. (4.66).The oven-drying temperature of 110 ± 5°C is suitable for most of the soils. A temperature more than 110 ± 5°C should not be used as it breaks the crystal structure of the soil and causes evaporation of structural water, which has properties completely different from normal water and is considered a part of soil solids.For soils containing gypsum or other minerals, there is loosely bound water of hydration (adsorbed water), which gets evaporated at 110°C. Hence, a lower temperature of 80°C should be used for oven-drying such soils. Similarly, for soils containing organic matter, the oven-drying temperature should not exceed 60°C to prevent oxidation of organic matter.The oven-drying method is the most accurate method of determining water content. The only disadvantage of the method is that it takes minimum 24 h to know the test result.2. Sand Bath Method:The principle for determination of water content in this method is the same as in the oven-drying method except that drying of the wet soil is done using a sand bath.Procedure:Water content is determined by sand bath method in the following steps:i. A clean dry non-corrodible container with lid is taken and its weight is determined (W1).ii. The required quantity of a representative undisturbed soil sample, is taken and placed loosely in the container. The weight of the container with lid and wet soil is determined (W2).iii. The container with wet soil is placed on a sand bath and is heated until all the water has evaporated. This takes about 0.5 to 1 h. The soil is mixed using a palette knife to ensure soil at the bottom is not overheated. Care should be taken to ensure that the sand bath is not too hot and does not exceed the temperature 110 ± 5°C. The container now containing dry soil is then cooled in a desiccator with the lid closed.iv. The weight of dry soil with the container and lid (W3) is determined. The water content is determined from Eq. (4.66).The sand bath method allows rapid determination of water content within 0.5 to 1 h. It is more suitable as a field test. The result obtained is less accurate than that obtained by the oven-drying method because there is no control over temperature during drying in this method. This method should not be used if it is suspected that the soil con­tains significant quantities of gypsum, calcareous matter, or organic matter.3. Alcohol Method:The principle of water content determination in the alcohol method is the same as in the oven-drying method except that drying of wet soil is done with the help of a methylated spirit.Procedure:Water content is determined by alcohol method using the following steps:i. A clean dry non-corrodible container with lid is taken and its weight is determined (W1).ii. The required quantity of a representative undisturbed soil sample, is taken and placed loosely in the container. The weight of the container with lid and wet soil is determined (W2).iii. The wet soil is mixed with a methylated spirit (1 mL/g of soil). The methylated spirit is worked well with the soil using a palette knife, and large lumps of soil, if any, are broken down.iv. The wet soil with methylated spirit is then ignited. The contents are constantly stirred with a spatula or knife, care being taken to ensure that none of the soil is lost.v. After methylated spirit completely burns away, the container (now with dry soil) is taken and cooled in a desiccator with the lid closed.vi. The weight of the dry soil with the container and lid (W3) is determined. The water content is determined from Eq. (4.66).4. Infrared Lamp Torsion Balance Method:This method enables rapid determination of water content of soils by employing a device providing infrared lamp for drying and torsion balance for getting percentage of water on wet basis from a scale. The results obtained are convertible to water content on dry basis.Apparatus:An infrared lamp torsion balance moisture meter consists of:i. An infrared lamp for drying wet soil.ii. A torsion balance for direct determination of water content.The infrared lamp is a 250-W lamp built in the balance and operates under a single-phase AC voltage of 220-230 V. Provision is made to adjust the input voltage to the infrared lamp to regulate the drying heat and temperature.The torsion balance has a built-in magnetic damper to reduce pan vibrations and is calibrated to give water content in the range of 1%-100% with a 0.2% least count. A thermometer graduated to read temperature from 40°C to 150°C is provided to monitor the temperature in the pan housing. A separate physical balance is not required to determine weights through this method.Procedure:Water content is determined by infrared moisture meter method using the following steps:i. About 25 g of a soil sample is taken. The lamp housing is raised and the soil is evenly distributed on the sample pan.ii. The lamp housing is then lowered and the infrared lamp is switched on.iii. A thermometer is inserted in its socket. The variac control knob is set between 95°C and 100°C. The soil sample now begins to lose water.iv. When the thermometer indicates a temperature of 105°C, the variac knob is adjusted in such a manner that there is no further increase in temperature.v. The drum scale is rotated by turning the drum drive knob until the pointer returns to the index. The percentage of water content is directly read from the scale. The final reading is taken when the pointer is steady on the drum scale, which indicates that the soil has dried to a constant mass.vi. The water content read from the scale is based on the initial wet weight of soil (ω’).It should be converted to water content (ω) based on the dry weight as follows:Water content based on the dry weight of soil, ω = Ww/WdWater content based on the wet weight of soil, ω’ = Ww/WSo we have –Thus, the water content based on the dry weight is computed as –ω = ω’/1 – ω’ …(4.67)The infrared torsion balance method allows rapid and accurate determination of water content. The result can be obtained in 15-30 min. The maximum size of particles in the soil sample should not be more than 2 mm because the quantity of soil sample used for test is 25 g.5. Calcium Carbide Method:The calcium carbide method is a rapid and reasonably accurate method of determination of water content of soil using a portable moisture content kit.The method is based on the principle that when the water in the soil reacts with calcium carbide, acetylene gas is produced and the pressure exerted by the acetylene gas on a diaphragm gives a measure of the water content.The water content obtained from the calcium carbide method is based on the initial weight of wet soil. It should be converted to water content based on the dry weight of soil.Procedure:Water content is determined by calcium carbide method using the following steps:i. About 6 g of a wet soil sample is taken for the test. Coarse-grained soils are ground and pulverized. Fine-grained soils are mixed with steel balls in pressure vessels to pulverize properly and to prevent formation of lumps of wet soil.ii. The soil sample is then placed in an air-tight container and mixed with a sufficient quantity of calcium carbide powder. The mixture obtained is shaken vigorously.iii. The acetylene gas produced by the reaction of the moisture of the soil with the calcium carbide exerts pressure on the diaphragm. The dial gauge located at the diaphragm reads the water content ω’ directly.iv. As the dial gauge is calibrated to read the water content based on the wet weight of soil, it should be corrected using Eq. (4.67).This method is very quick and the result can be obtained in 5-10 min. The method is more suited as a field method of water content determination for compaction control where water content is to be quickly determined. Care should be taken to ensure that the wet soil-calcium carbide mixture is not exposed to air as calcium carbide will then react with the moisture in air and as a result, the water content of the soil will be overestimated.6. Pycnometer Method:The pycnometer method is a rapid method of water content determination for soils whose specific gravity is accu­rately known. The method is suitable for coarse-grained soils only as the entrapped air is likely to cause a signifi­cant error in water content determination for fine-grained soils.Pycnometer is a density bottle of 900 mL capacity. A brass conical cap is used as a cover. The conical cap is always screwed to the pycnometer up to the mark on the pycnometer to give the designated volume of 900 mL. A rubber washer is placed inside the conical cap to prevent the leakage of water through the walls of the pycnometer and the conical cap.Procedure:The principle of water content determination by pycnometer method is illustrated in Fig. 4.16.i. The weight of a clean and dry pycnometer with the cap is taken and recorded (W1).ii. About 200-400 g of a wet soil sample is placed in the pycnometer and the weight of the pycnometer with cap and wet soil is taken (W2).iii. Water is added to the pycnometer in increments and the contents are mixed using a glass rod. Care should be taken to remove the entrapped air completely by mixing the contents thoroughly. A vacuum pump may also be used for this purpose.iv. The pycnometer is then completely filled with water up to the hole in the conical cap. The outside surface of the pycnometer is wiped with a cloth. The weight of the pycnometer with wet soil and water is taken (W3).v. The contents of the pycnometer are then removed and the pycnometer is washed thoroughly. The pycnometer is again filled with water completely up to the hole in the conical cap. The outside surface of the pycnometer is wiped with a cloth and the weight of pycnometer with water is taken (W4).vi. The water content of the soil is computed using the following equation:The advantage of the pycnometer method is that drying of the soil is not required for determination of water content. However, entrapped air can become a source of serious error in this method. Also, the accuracy of the water content obtained through this method is dependent on the accuracy of the specific gravity used in calculations. The method is not recommended by IS – 2720 (Part 2) – 1973, which is the code of practice for water content determination.Derivation of Expression for Water Content in Pycnometer Method:Referring to Fig. 4.16, water content will be –ω = Ww/Wdand the weight of water in wet soil will be –Ww = (W2 – W1) – WdHere, W2 and W1 are known.The weight of dry soil (Wd) is determined as follows:G = γs/γw = Wd/Vsγw ÞVsγw = Wd/G