# More handshakes than you can shake a stick at…

Mr and Mrs Smith’s dinner party was a fantastic success. At the next one there was, naturally, a lot of discussion about hand shakes. Which leads us to the next challenge:

It is claimed that there must always be at least two people in the world who have shaken hands the same number of times.

Is this true? Or false? Prove it.

(h/t Anupam Das)

# Another game we can play…

The goal of this game is to make 21. You have the four numbers 1, 5, 6 and 7 and you can use any combination of multiplication, addition, division, subtraction and bracketing. And that’s it, that’s all there is to it.

I know of one solution, and with a slightly charitable interpretation of the question found two more. There could be others.

Edit: Any solution must use each of the numbers 1, 5, 6 and 7 exactly once each

# A game we can play

Here is a sequence of numbers:

• 2, 4, 6

What is the rule for generating the next number? If you post a comment I’ll tell you if it’s right or wrong, and if you post another sequence of numbers I’ll tell you if it fits the generating rule.

PS: Don’t google this one, that kind of spoils it 🙂

# One mathematician’s beautiful test

Aptitude tests have a bad rep. So why am I posting one to my puzzles blog? Especially since it’s not even a new one, instead first crafted by Jim Propp and posted online in 2002. Why?

# Halving to double – a puzzle

A prisoner was attempting to escape from a tower. He found a rope in his cell that was half as long enough to permit him to reach the ground safely. He divided the rope in half, tied the two parts together, and escaped. How did he escape?

# Great sheets of gold!

Imagine you live in a world where value is represented by physical items. Not diamonds or gold bars, that would be impractical, but pieces of paper and especially small discs of metal or plastic. Call these strange discs “coins”.

# Why?

Why qua locus puzzle? There are six reasons that make two.

Page 411 of “Foundations of Psychology”, by Nicky Hayes