Lewis Carroll, who died 125 years ago on Saturday, was perhaps the world’s greatest populariser of logical puzzles. His most famous book, Alice in Wonderland, is a masterclass in how to turn arcane mathematical logic into whimsy and humour. Today’s challenges begin with a little known conversation between two of Carroll’s best-loved characters.
1. A handy chat
Cheshire Cat: Okay Alice, let us call a whole number ‘handy’ if its digits add to a multiple of 5. Can you think of a handy number?
Alice: Why I can think of plenty! 14, 55, 406, 77777…
CC: Very good! But your examples are all quite far apart. How close together do you think two handy numbers can be?
Alice: Well… 55 and 64 are both handy, and they’re pretty close. Will that do?
CC: I think you can do better than that.
Alice: Let me think…
What’s the best you can do?
2. A cardy convo
Four cards numbered 1, 10, 100 and 1000 lie face down on a table. The cards are distributed between three truth-tellers and one liar, with each person receiving one card. Then the four of them speak one after another:
“My number is odd.”
“My number has 3 digits.”
“My number is less than 100.”
“My number is more than 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 conundrums were written by Daniel Griller, a British puzzle setter. His latest book, A Ring of Cats and Dogs, is out now.
PLEASE NO SPOILERS Instead discuss Lewis Carroll.
I’ll be back at 5pm UK with the answers.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.
