Can you solve it? The poker puzzle that has everyone fooled | Mathematics

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Today’s two puzzles are from my new book Think Twice: Solve the Simple Puzzles That (Almost) Everyone Gets Wrong.

As readers of this column will know, I love a counter-intuitive puzzle, i.e. when the obvious answer is not the correct one.

But then again, today I may be bluffing. You have been warned.

1) Pint-sized problem

Which is longer? a) the height of this pint glass, or b) the circumference of its rim?

Comment: you may have seen this question in the context of classic UK pint glasses, but I am asking about continental style pint glasses, which are much thinner and higher.

2) Fool House

You are playing poker. Which is the stronger of the two hands below?

Two full houses: AAAKK and AAA99

For clarification, the highest ranked poker hands are, in order from the strongest, royal flush, straight flush, four-of-a-kind, and full house. When two hands of the same rank face off, the winner is the hand with the cards of highest value. (For a more detailed description of the ranks see below.)

The poker puzzle is one of my favourites. I’ve never met anyone who has got it right. Don’t let me down!

I’ll be back at 5pm UK with the answers. Meanwhile NO SPOILERS. Please discuss imperial measurements, sand-based receptacles or card games.

If you enjoy counter-intuitive conundrums, I hope you will find much to love in Think Twice. The puzzles are fun to solve in a group – maybe over a pint, or a game of cards.

Poker definitions: a royal flush is a run of AKQJ10 in a single suit, a straight flush is any other run of consecutive cards in the same suit, a four-of-a-kind is a hand with all four cards of the same value, and a full house is two of one value and three of the other.

Think Twice cover

Think Twice: Solve the simple puzzles (almost) everyone gets wrong (Square Peg, ££12.99). 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.

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