Stage Four
Crowned
Prince Charming was suspicious of his crown makers. He suspected that they were not using all the gold that he provided to make his crowns. He decided to test the crown makers. He ordered three different crown makers to make identical crowns for him. He had each crown maker think that only one crown was being made.
How could he discover which of the crown makers were cheating him?
What problems might occur to make his task difficult?
Hint: He has at least one crown maker who is not dishonest.
Reference: Signpost Mathematics Year 7
A McSeveny/R Conway/S Wilkes, Longman p50
If he supplies all the crown makers with the same amount of gold, and knows that at least one of them is not cheating him, then by comparing the weights of the crowns made he would be able to determine which is the heaviest. The one that were lighter than that would be made by dishonest makers.