Lewis Carroll, who died 125 years ago on Saturday, was perhaps the world’s greatest popularizer of logic puzzles. His most famous book, Alice in Wonderland, is a masterclass in how to turn arcane mathematical logic into fantasy and humor. Today’s challenges begin with a little-known conversation between two of Carroll’s most beloved characters.
1. A Practical Conversation
Cheshire Cat: Ok Alice, let’s call an integer “handy” if its digits add up to a multiple of 5. Can you think of a handy number?
Alice: Why can I think of so much! 14, 55, 406, 77777…
CC: Very good! But your examples are all quite far apart. How close do you think two practical numbers can be?
Alice: Well… 55 and 64 are convenient, and they’re pretty close. Will it do?
CC: I think you can do better than that.
Alice: Let me think…
What can you do better?
2. A cardy convo
Four cards numbered 1, 10, 100 and 1000 are placed face down on a table. The cards are divided between three truth tellers and one liar, with each person receiving a card. Then the four speak one after the other:
“My number is odd.”
“My number has 3 digits.”
“My number is less than 100.”
“My number is over 100.”
What number was on the liar’s card?
(Clarification: Truth tellers always tell the truth and liars always lie.)
Both of today’s Carrollian puzzles were written by British puzzler Daniel Griller. His latest book, A Ring of Cats and Dogs, has just been released.
PLEASE NO SPOILERS Discuss Lewis Carroll instead.
I’ll be back at 5pm in the UK with the answers.
I install a puzzle here every two weeks on a Monday. I’m always on the lookout for great puzzles. If you want to suggest one, write to me.
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