Check out the answers to Brain Teasers from Automation Notebook below:
Qualified Distributions Answer
Starting with the lead electrician, the starting (and ending) lug quantities must have been 12,10,8,6,4,2,0.
To reason this though, start with the last electrician – they must be left with 0 lugs, because the last redistribution is for THAT last electrician to give all their lugs away (evenly!). Then consider the next-to-last electrician, they had just given all their lugs away on the previous distribution, so at the end they would be left with only 1/6 of whatever the last electrician had before the final distribution. In a similar fashion, the fifth electrician ends up with just 2 amounts, one from 6 and one from 7. This suggests that the pattern must be a decreasing series from the lead electrician down to the 7th. Since we are only dealing with “whole” lugs and not factions of lugs, then the minimum sequence possible is 6,5,4,3,2,1,0 – but that only adds up to 21 lugs. Double all those values for a decreasing series that totals 42 lugs.
Slow Fuse Answer
Light any three ends of the two fuses simultaneously. When the first fuse burns out completely, immediately light the fourth (last) end. When the second fuse is gone, 45 secs will have elapsed.
The first fuse will finish it’s burn after 30 seconds – although that may happen in the center of the fuse. At that point there will be 30 seconds of fuse left to burn on the second fuse (although that may not be exactly half of the length of the fuse). Lighting the other end will shorten that 30 second burn to 15 seconds, for a total of 45 seconds.
Triangle Tangle Answer
The five images here detail 6 unique triangles (labeled A through F) which are duplicated 12 times each in the symmetrical patterns shown, for a total of 72 total triangles.
