Can you solve it? Lewis Carroll fan fiction

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.