Earlier today I set you the following counterintuitive puzzle, about a curious object that fits through a small hole, but not through a big one. Here it is again with solutions.
Less is more
Design an object that cannot pass through an open window, but can pass through one that is almost half shut.
Here are illustrations of a cross-section of the window that make it clear what is required. The wall is blue, and the two casements are orange.
Solution
Here are three objects that fit the bill. They all pass through by curving around the closed (or almost closed) casement. The simplest shape has a cross section of three sides of a square:
(If anyone is looking for some homework, perhaps someone could calculate the precise dimensions of the shape, in relation to the width of the window, the thickness of the casements and the angle of the partially shut casement, and post them below?)
The V-shape also works:
The C-shape is possibly the most elegant. Here are two videos showing how it cannot get out the open window, but can when one of the casements is flush with the wall.
Thanks to Kvantik, a Russian maths magazine for schoolchildren, for today’s puzzle.
One final thing: my new book is out on Thursday. Think Twice is a compilation of counterintuitive puzzles together with explanations of why they trip us up. If you enjoyed today’s challenge, I am sure you will enjoy it!
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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