Earlier today I presented you with these two puzzles, which are excerpts from my new book Think twice: solve the simple puzzles (almost) all get wrong. Here they are again with solutions.
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 British pint glasses, but I’m asking about continental style pint glasses, which are much thinner and taller.
Solution b) The edge is longer.
Next time you’re in a bar, ask anyone this question. They always will says the height. But with a traditional pint glass, the circumference is almost twice as long as the height. Even with this ultra-sleek Peroni glass, the rim pushes it. It doesn’t seem like it’s true, but it is.
The circumference of a circle is pi (3.14 to two decimal places) times the diameter. The diameter of a Peroni glass is 76 mm, giving a circumference of 238 mm. The height is only 231 mm.
The moral of the story: people are very bad at intuitive outlines. We are used to measuring lengths as straight lines. When we see a glass side, we look left to right and back again. But the circumference is not double the diameter – it is more than three times as long. Don’t forget the pi in pint!
2) Fool House
You play poker. Which is the stronger of the two hands below?
For clarification, the highest ranking poker hands are, in order of 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 highest value cards. (For a more detailed description of the ranks see below.)
Solution b) is stronger.
People here fall into the trap of thinking that I am asking which hand is stronger when the hands are playing against each other. If this were the case, the first hand would be stronger because it has the higher value cards.
However, they cannot play against each other! Poker use a single deck and there are only four aces are total. If one player has the first hand, no one has the second hand, and vice versa.
The meaning of ‘stronger’ in the context of the puzzle is the hand that puts a player in the stronger position in a game. Perhaps a more succinct setting of the puzzle is ‘Which hand would you rather be dealt?’
Both hands are equally strong against other full houses and four-of-a-kind. But AAA99 blocks more straight flushes, as this means an opponent cannot have 5-9, 6-10, 7-J, 8-Q, or 9-K. The AAAKK only blocks 9-K.
The effect is only marginal (perhaps a reader will want to calculate the percentages) but it is there!
I hope you enjoyed these puzzles. If you did, Think twice have much more. The book is just out, and – dare I say Christmas? – it would be a perfect gift. The puzzles are designed to be fun when solved as a group.
Thanks to Shoma Amin from Asahi UK.
Poker definitions: a royal flush is a run of AKQJ10 in a single suit, a straight flush is any other series of consecutive cards of 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: Solve the Simple Riddles (Almost) Everyone Gets Wrong (Square Peg, £12.99). To support the Guardian and Observer, order your copy from guardianbookshop.com. Delivery charges may apply.
I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want to suggest one, email me.
