Q.Try out the 'water in three bottles' activity with your friend. There are three bottles, A, B, and C. Bottle A can hold 21 ml., B can hold 127 ml., and C can hold 3 ml. The task for your friend is to get 100 ml of water with the help of these three bottles. There are six more problems like this.

For the given problem, filling B completely and pouring out through A once and C twice leaves exactly 100 ml in B — this same B minus A minus 2C method works for the first five problems in the set, but problems 6 and 7 are deliberately designed so that a much simpler method (just A minus C) works instead, to test whether a mental set has form …

This activity, drawn directly from the chapter, is designed to let a person observe a friend forming — and then getting trapped by — a mental set. For the stated problem, filling bottle B completely (127 ml) and pouring from it into A (21 ml) leaves 106 ml in B; pouring from B to fill C (3 ml) and discarding it leaves 103 ml; pouring from B to fill C once more leaves exactly 100 ml in B. This same sequence, B minus A minus (2 times C), also solves problems 1 to 5 of the set the chapter refers to.

The chapter explains that problems 6 and 7 are deliberately constructed so that this same well-practised B minus A minus 2C sequence still technically works, but a far simpler method — simply pouring from A into C once (A minus C) — also reaches the target and does not need bottle B at all. Someone who has just solved problems 1-5 using the standard sequence typically keeps applying it out of habit to problems 6 and 7 as well, failing to notice the shortcut sitting in plain sight — a direct, hands-on demonstration of how mental set, built up …