Today’s first puzzle was penned by Randall Munroe, cartoonist of the webcomic xkcd and author of the bestselling book What If?
For the (surely) very few readers who have never heard of him, Munroe, a former NASA roboticist, is probably the world’s premier science humorist.
Today’s challenge, a riff on his classic cartoon about self-reference, is both a puzzle and a meta-joke.
1. All Together Now
Find all the possible ways, if any exist, to fill in the three blanks to make all three statements true.
Today’s second puzzle is an elegant take on the Venn diagram. It was written by RGee Watkins, a maker of wooden block puzzles.
2. One to Venn
The four squares below form a Venn diagram with ten regions, labelled A to J. The letters A to J each stand for a number between 1 and 10, such that no two regions share the same number and all numbers from 1 to 10 are used. The regions in each square add up to the same number. What value is D, the intersection of all four squares?
I’ll be back at 5pm UK with the solutions. Please NO SPOILERS! Instead talk about your favourite Munroes, Munros and Monroes.
Both of today’s puzzles are taken from The Mathematical Playground: People and Problems from 31 Years of Math Horizons. Math Horizons is the undergraduate magazine of the Mathematical Association of America, and the book, a compilation of its best puzzles, is full of great material. For more information see here.
What If? (10th anniversary edition) by Randall Munroe will be out in the UK on November 14.
My latest book is Think Twice: Solve the Simple Puzzles (Almost) Everyone Gets Wrong. (In the US it is called Puzzle Me Twice, and out tomorrow.) To support the Guardian and Observer, order your copy at guardianbookshop.com. Delivery charges may apply.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.