F 1120 2012: Fill & Download for Free

Here's a nice solution that was shown to me long ago. (I would never have figured this one out by myself.)Here's the algorithm for solving the 12 balls in three weighingsproblem. It also happens to solve the 3 balls in two weighings or 39balls in 4 weighings, or 120 balls in 5 weighings or ..., problems.First, list all 3 digit combinations of 0, 1, and 2:000 100 200001 101 201002 102 202010 110 210011 111 211012 112 212020 120 220021 121 221022 122 222(For the 4 weighing problem, list all 4 digit combinations, and so on.)Next, cross out all sets with identical digits (000, 111, 222), and alsothrow out all whose first digit change (reading from left to right) isnot 01, 12, or 20. In other words, 112 is left in because the firstchange is from 1 to 2, but 212 is eliminated, since the first change isfrom 2 to 1. This leaves:(a) 001(b) 010(c) 011(d) 012(e) 112(f) 120(g) 121(h) 122(i) 200(j) 201(k) 202(l) 220where a, b, ..., l are the balls.Now, for the first weighing, weigh all the balls with a 0 in their firstposition against all the balls with a 2 in the first position, in otherwords, (a, b, c, d) are weighed against (i, j, k, l). If the balls withthe 0 are heavier, write down 0; if the balls balance, write 1,otherwise; write 2. Next, weigh all balls with a 0 in the secondposition against all balls with a 2 in the second position (a, i, j, k)against (f, g, h, l), and write down the digit corresponding to theresult of the weighing, and do it again for the third position in thethird weighing.As an example, suppose ball f (120) is heavy. In the first weighing, fis not involved, so write down 1. Next, (f, g, h, l) -- the "2" ballsare heavier than (a, i, j, k) so write down 2. Finally, in the weighing(b, f, i, l) versus (d, e, h, k), the "0" side (b, f, i, l) is heavier,so write down a 0. You have written "120" -- the code for ball f -- sof is the heavy ball.If you find that the combination you write down is not in the list, say211, then change the 2s to 0s, the 0s to 2s, and leave the 1s alone,giving 011. This is ball c, but since you had to flip the digits, ballc is lighter.With N weighings, there are 3^N combinations, of which we eliminate 3and cut the remainder in half, so for 4 weighings, one can distinguish(3*3*3*3-3)/2 = 39 balls, etc.In general, if you have n weighings, you can distinguishamong (3^n - 3)/2 balls and find the one that is either lightor heavy.The (3^n - 3)/2 is easy to explain. In each ball's "name"there are n slots to fill, each of which can be any of 0,1 or 2, so there are 3^n of those possibilities. But00...0, 11...1, and 22...2 are tossed out, so thereremain 3^n-3. This has to be divided by 2, since eachball really has two names -- one meaning "heavier" andthe othe meaning "lighter".Here is a list of the 39 names for lighter balls:1 00012 00103 00114 00125 01006 01017 01028 01109 011110 011211 012012 012113 012214 111215 112016 112117 112218 120019 120120 120221 121022 121123 121224 122025 122126 122227 222028 220029 220130 220231 200032 200133 200234 201035 201136 201237 202038 202139 2022Here are the weighings:1 2 3 4 5 6 7 8 9 10 11 12 13 <-> 27 28 29 30 31 32 33 34 35 36 37 38 391 2 3 4 31 32 33 34 35 36 37 38 39 <-> 18 19 20 21 22 23 24 25 26 27 28 29 301 5 6 7 18 19 20 28 29 30 31 32 33 <-> 11 12 13 15 16 17 24 25 26 27 37 38 392 5 8 11 15 18 21 24 27 28 31 34 37 <-> 4 7 10 13 14 17 20 23 26 30 33 36 39Suppose ball 21 is heavy. The results of the weighings willbe:equalright heavyequalleft heavyThis codes to 1210 which is ball 21.If ball 32 is light, here's what you'd get:left heavyright heavyright heavyequalThis codes for 0221 which does not appear in the list. Thusthe indicated ball is light, not heavy and has code 2001 whichis ball 32's code.

It may seem that way to the casual consumer, but it’s simply not true and there is nothing unusual happening here. It’s just the diverse lens industry conducting business as usual.Manufacturers, especially ones with a large consumer base, have to satisfy various different categories of customer, each with a different buying profile and priorities; mid-range, enthusiast, professional, specialist.This is why you can already buy lenses ranging from $100 to $50,000, there’s nothing new in this respect for the RF lenses.Take the 24–105/4L USMCanon EF 24–105/4L USM - Launched: 2003 - $1250Canon EF 24–105/4L USM II - Launched: 2016 - $1100Sony FE 24-105mm f/4 G OSS - Launched 2017 - $1299Canon RF 24–105/4L USM - Launched: 2018 - $1099So for the 24–105, it’s launched cheaper than the original EF version did 15 years ago, cheaper than the Sony equivalent, and it regularly gets a $200 discount down to $899 when bought as part of a kit.The reviews have been universally excellent and it has gained a well earned reputation for being sharp across the whole frame, at all focal lengths, even wide open.In addition to the excellent performance, it uses the new nano-USM motor upgraded for L class lenses for the first time. nano-USM combines the smooth fast silent focusing of STM (particularly important to videographers) with the expected fast accurate focusing of USM.Further, it uses an upgraded optical image stabilisation system and has the extra (third) control ring feature of the RF lenses, and naturally being an L lens, it is weather sealed and built for durability.In summary, if $1099 is a lot of money for you, it will be considered expensive, but for its performance and place in the range and the industry, it’s actually good value.Next, the 35mm Prime.Canon EF 35mm f/2 - Launched: 1992 - $400Canon EF 35mm f/1.4L USM - Launched: 1998 - $1420Carl Zeiss Distagon T 35mm f/2 ZE - 2009 - $1030Carl Zeiss Distagon T 35mm f/1.4 ZE - Launched 2010 - $1843Canon EF 35mm f/2 IS USM - Launched: 2012 - $850Carl Zeiss Milvus 2/35 ZE - Launched: 2015 - $1120Canon RF 35mm f/1.8 IS Macro STM Lens - Launched: 2018 - $499Here we see Canon introducing a mid-range lens. And again it’s a really nice one which takes full advantage of the new mirrorless form factor, for example it uses a reversed design with the smaller element at the front and the larger element at the rear, protected in the body.Being a midrange lens means balancing compromises and I think they made very good decisions here. It’s a bright f/1.8 lens that gives reasonable resolution wide open, but needs to be stopped down for best performance. The wider aperture will be useful indoors for capturing casual moments, while outdoors it can be stopped down to deliver maximum performance.In the early days of the m43 system Panasonic released a 20mm F/1.7 pancake lens with very similar characteristics; convenient size, useful bright apertures and very good performance stopped down. It proved to be very popular and highly cherished lens for the system and I’m confident this 35mm f/1.8 will occupy a similar role for midrange R system users.Panasonic Lumix G 20mm F1.7 ASPH - Launched 2009 - $400The 35/1.8 has an STM motor and it’s a macro too, and as an RF lens it has the extra control ring.So next, what about a ~50mm Prime.Canon EF 50mm f/1.4 USM - Launched: 1993 - $385Canon EF 50mm f/1.2L USM - Launched: 2007 - $1574Carl Zeiss Planar T 50mm f/1.4 ZE - Launched: 2009 - $725Carl Zeiss Makro-Planar T 50mm f/2 ZE - Launched: 2009 - $1280Carl Zeiss Distagon T* Otus 1.4/55 ZE - Launched 2013 - $3999Canon EF 50mm f/1.8 STM - Launched: 2015 - $125Carl Zeiss Milvus 1.4/50 ZE Canon - Launched 2015 - $1200Sony FE 50mm F1.8 - Launched 2016 - $250Sony Carl Zeiss Planar T* FE 50mm 1.4 ZA - Launched 2016 - $1500Canon RF 50mm f/1.2L USM - Launched 2018 - $2300Perhaps nothing shows the diversity of lens buyers more than the fast 50mm primes, with options ranging from $125 to $4000.It’s a very important lens with many different price points but it is also perhaps the hardest for some to understand, why one costs $125, another costs $1000 and yet another costs $4000.Some people (often people who haven't found their own niche(s)) want to have an entire collection of lenses covering every conceivable focal length from 10mm to 1000mm, and with fast apertures too. I suspect the reasons are a combination of fear of missing out (FOMO) and/or not having discovered their niche yet.Such people will put a lot of effort into comparing features in the belief that their is exactly one correct choice. Unless the budget is not a factor, it’s hard to see this market choosing a $4000 50mm. They are more likely to choose a cheaper 50mm and put the money to other lenses.But there are others who are happy with a single lens, or perhaps a small set, or perhaps price is not the critical factor. Perhaps they are a working photographer who takes the same shots day in and day out using their tried and trusty lens.They know precisely what works for them, and why, and may well understand that seemingly small differences in performance specifications may not tell the whole story. For them, a peak performance $2000 or $4000 50mm may be a necessity before they will even take a system seriously.So the answer is simple. People are different. They see things differently and make different choices in line with different priorities. It may sound like a mundane and somewhat unsatisfying conclusion, but actually, diversity is great, and the simple fact is:There is a market for the $100 50mmThere is a market for the $1000 50mmThere is a market for the $2000 50mmThere is a market for the $4000 50mmAlthough Minolta made the first move, when Canon introduced their EOS system in 1987, it heralded the dawn of electronically controlled cameras. Eos is the name of the goddess of the dawn in greek mythology.Canon were not the dominant force in the industry back then, and they saw embracing the the benefits of electronics to control auto focus and apertures as a strategy to grow the business.To showcase this new era they announced the now legendary EF 50 f/1.0L USM which was released in Japan in 1989 for ~$2000.It was technologically way ahead of anything else at the time with a very complex optical formula and equally complex electro-mechanics to operate it.Making such a showcase lens was a sign of Canon’s belief in the EF/EOS system and the benefits the system delivered were not lost on the market; the sports and news segments in particular, and so began Canon’s rise to dominance.The lens was discontinued by 2000 as the much cheaper mid-range 50/1.4 USM, released 1993, was deemed good enough by many and so impacted the 50/1 sales.Much of the electro-mechanical design of the 50/1.0L lives on today in the form of the EF 85/1.2L, while the original EF 50/1.0L USM has acquired legendary status and still sells on auction sites for ~$3000–4000.As an EF USM lens it still fully compatible with the new EOS R series (with an EF to R adapter) but finding a sharp copy seems pretty rare these days as they haven't been serviced for almost 20 years.Check out Ken Rockwell’s loving ode to it here: Canon 50mm f/1.0 ReviewLens rentals recently got hold of a copy and subjected it to their ultra-high tech analysis where it put up a technically mediocre (by todays standards) performance, but that was almost certainly due to being de-centred (likely due to getting knocked about in use and not being serviced). Despite this, the renderings of the sample shots still have a somewhat unique beauty to them.It seems completely fitting that, in addition to a mid-range and enthusiast range lenses, Canon mark the launch of EOS R era with some real high prowess lens building.Given their history, the choice of RF 50/1.2L USM and RF 85/1.2L USM makes complete sense, while the insanely specified RF 28–70/2.0L USM seems more akin to a wake-up call for those who thought Canon were sleeping.

I have 3 inline 6’s.1992 Ford F-150 with a 4.9L/300″ inline 6 145 hp@3400 rpm / 265 lb-ft@2000 rpm2018 BMW K1600 GTL with a 1649cc/100.6″ Inline 6 160 hp@7750 rpm / 129 lb-ft@5250 rpm (226 lbs including clutch and gearbox)2012 Ram 2500 with a 6.7 Cummins inline 6 350 hp@3013 rpm / 610 lb ft@1500 rpm. (1120 lbs dry)As you can see they vary HUGE from hp to torque (and weight)