One of the puzzles in the MathsJam Shout looked impossible, so obviously I sat down with Mr Miller and had a go at it.
I don't have it in front of me, but it went something like:
A couple hosts a party to which five other couples are invited. At some point in the evening, hands are shaken. Afterwards, one of the hosts asks everyone else how many hands they shook and discovers:
- Nobody shook hands with everyone else.
- Nobody shook hands with their partner (or with themselves).
- Everyone he asked shook a different number of hands.
How many hands did the host's partner shake?
Take a moment to have a crack at it, if you like. Don't read beyond the horizontal line, unless you like spoilers.
We drew pictures. We frowned a lot. Mr Miller may have sworn a little bit, but not me.
We figured it out as follows:
A lovely puzzle. Did you solve it a different way? Let me know!