The Master Theorem

In case you have never heard about “the secret society of puzzle solvers” at The Master Theorem, then get ready to face about 50 of the most creative, challenging and original puzzles you can find on the web. Even though the website rarely has been updated in the last few years, it can offer tens of hours of problem solving to all newcomers. In order to sign up and explore everything TMT has to offer, you must first complete one of the numerous puzzles posted there. An easy one you can start with is “Old McDonald”, which can be solved using this… SPOILER.

King Octopus and His Servants

King Octopus has servants with 6, 7, or 8 legs. The servants with 7 legs always lie, and the servants with 6 or 8 legs always tell the truth. One day four of the king’s servants had the following conversation:

“We together have 28 legs,” said the first octopus.
“We together have 27 legs,” said the second octopus.
“We together have 26 legs,” said the third octopus.
“We together have 25 legs,” said the fourth octopus.

Which of the four servants told the truth?

If all four octopuses lied, then their total number of legs must be 28, which is impossible. Therefore exactly one of them said the truth, and the other three had 7 legs each. Since the truthful octopus must have 6 or 8 legs, and 21 + 8 = 29, we see that it has exactly 6 legs, and therefore it is the second one.

The Magnetic Rod

You are in a room with nothing else but two indistinguishable iron rods. You know that one of them is magnetized, how can you figure out which one?

Touch the middle of the first rod with the end of the second rod. If the two rods get attracted to each other, then the second one is the magnet. If not, then the first one is the magnet.