July 13, 2024

Earlier today I asked you to Nice thinking about the following puzzles. (This is the name of my new book, about mysteries that often catch us.)

1. Hello ducklings

There are two ducks in front of two ducks, two ducks behind two ducks and two ducks in between. What is the minimum number of ducks?

Solution. 4 ducks.

Most people answer 6 ducks because they assume that the two ducks are next to each other, like the bottom left. In fact, if there is a line of 4 ducks in single file, like the bottom right, it is also the case that the statement in the question is true.

2. Concentric puzzle

Imagine I’m walking around a circle whose center is Big Ben. For the purposes of this question, assume I can walk on water.

When the radius is 1 km, I will walk approximately 6.28 km

When the radius is 100 km, I will walk approximately 628 km

When the radius is 10,000 km, I will walk about 62,800 km?

(The circumference of a circle is twice the radius times pi, which is 3.14 to two decimal places.)

Solution No!

The largest circle it is possible to walk around Big Ben is the circumference of the Earth, which is approximately 40,000 km.

3. Hanging from a rope

A bottle of water hangs from the ceiling by a rope. A handle hangs from the bottle by a piece of the same type of rope, as shown below.

You pull the handle off. A string breaks. Which one?

a) the top one

b) the bottom one

c) they break at the same time

Solution It depends!

If you pull the string slowly, the top one will break. If you give it a quick tug, the lower one will.

When you pull slowly, the top rope breaks first because it has more force acting on it: the downward force of the bottle as well as the downward force of the hand.

When you pull quickly, the bottle won’t have time to move down enough (and stretch the top string) before the bottom string breaks.

I chose these puzzles because they fit my definition of ‘simple puzzles that almost everyone gets wrong’. They are easy to name, the answer is not difficult to work out, and yet people rarely come up with the correct answer at first glance.

My new book Nice thinking Puzzles has 70 puzzles of this type, with examples from mathematics, physics, geography, psychology and the science of illusion. It’s out on September 5th in the UK and October 22nd in the US. If you enjoyed today’s puzzles, please consider pre-ordering!

Think twice: Solve the simple puzzles (almost) everyone gets wrong by Alex Bellos (Square Peg, £12.99). To support the Guardian and Observer, order your copy from guardianbookshop.com. Delivery charges may apply.

Thanks to Fabio Ciuffoli, who first told me about the ducks, and Nikolai Andreev, who told me about the circles.

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.

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