Earlier today I asked you to Think Twice about the following puzzles. (It’s the name of my new book, on puzzles that often catch us out.)
1. Hello duckies
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 are assuming that the two ducks are next to each other, as below left. In fact, if there is a line of 4 ducks in single file, as below right, it is also the case that the statement in the question is true.
2. Concentric conundrum
Imagine I am walking around a circle whose centre is Big Ben. For the purposes of this question, assume I can walk on water.
When the radius is 1 km, I will walk roughly 6.28km
When the radius is 100km , I will walk roughly 628km
When the radius is 10,000km, will I walk roughly 62,800km?
(The circumference of a circle is twice the radius times 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 about 40,000km.
3. Hanging by a string
A bottle of water hangs from the ceiling by a string. A handle hangs from the bottle by a piece of the same type of string, as below.
You pull the handle down. 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 jerk, the bottom one will.
When pulling slowly, the top string 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 fast, the bottle will not 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 state, the answer is not hard to work out, and yet at first glance people rarely come up with correct answer.
My new book Think Twice puzzles has 70 puzzles of this type, with examples from maths, physics, geography, psychology and the science of illusion. It is out on September 5 in the UK and October 22 in the USA. If you enjoyed today’s puzzles, please think about 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 at 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 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.
