Maths prize 24 Jan: how tough is the smartphone?
A new smartphone will survive being dropped several storeys. But how many? A 64-storey drop will smash it. Given a 64-storey building, how can you find the exact maximum drop in just six experiments? And how many phones do you need for that?
Mohaned al-Bassam, Howard Tran, and Helen Hoang won prizes.
You do it in six experiments by halving the range of storeys surveyed each time.
First time you narrow it down to 32 storeys by dropping a phone from 32nd floor
Then to 16 storeys, then to 8, then to 4, then to 2, then to 1.
You need a maximum of six phones.
The principle here, of halving the problem each time, is similar to QuickSort in Decision Maths and interval bisection in Numerical Methods.