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Choose a guard and ask him, If you choose the truthful guard, he will give you an honest answer. Enter his door if he says "yes" and enter the other door otherwise. If you choose the liar, he wil …

Assumptions: it is possible to "duplicate" a container by pouring liquid into an empty container until it has exactly as much liquid as the original. it is possible to "average" two containers by po …

Bob "peels" each pylon, effectively seperating the inside from the outside. If he has a long enough knife, he can do this without leaving any visible cuts. Here is a depiction of the cross section of …

(assuming numbers with leading zeros, ex "05" are forbidden) Part 1. Establishing an upper boundary for digit size Suppose there exists a solution where the largest blank is filled in with three d …

I got: Here's how I found the first 15 or so values. (terminology note: when I say a group is (x,y,z), that means the group must contain those numbers, but we don't know in what order yet)

This is a restatement of Hilbert's paradox of the Grand Hotel, in particular the Infinitely many coaches with infinitely many guests each problem. The solution is to take each person's ticket, and as …

Not necessarily. That is a reply that could be made by an insane patient. Anything an insane inhabitant says is false. When an insane inhabitant says "I believe [X]", then the truth is that he does n …

I wrote a script to go through all possible equations using +, -, /, *. Here is the output: 7 7 * (3 - (40 / 20)) (3 - (40 / 20)) * 7 7 / (3 - (40 / 20)) 40 40 * ((3 * 7) - 20) 40 * ((7 * 3) - 2 …