Find the fake
There are 12 identical looking coins, one of which is a fake. The
counterfeit coin is of a different weight to the rest. What is the
minimum number of weighings needed to locate the fake coin?
Age
14 to 16
Challenge level
Problem
There are 12 identical looking coins, one of which is a fake.
The counterfeit coin is of a different weight to the rest.
Using only a simple balance, what is the minimum number of weighings needed to locate the fake coin and how is this done?
Student Solutions
This proved quite a challenge! It was Helen (Maidstone Girls' Grammar) and Joel (of ACS in Singapore) who correctly found that only 3 weighings are needed.
Here is one way to solve the problem. We've labelled the coins ABCDEFGHIJKL.
Image
At West Flegg Middle School Polly and Rebecca found a method for 4 weighings, as did Michael (Cranmore Primary School, in Perth, West Australia).