Question

(Find the Fake). You are given 7 gold coins that appear to be identi- cal, but one is a fake and weighs slightly less than the other 6. You are also given a balancing scale. Find a way to determine which coin is that fake by using the scale only twice. Give a carefully writ- ten explanation of your solution.

Answer 1

among the 7 gold coins given

first try to put 3 in one pan and the other 3 in the other pan

if both are showing the same weight then we are done the left one is the less weight one

otherwise we will have less weighing in any one pan

suppose if they are less weighing in pan 1 there will be 3 coins

so choose any two coins from the 3 and put each in one in 1st pan the other is 2nd pan

if both are equally balanced then the left one is the fake gold coin

other case is that we will have one pan weighing less the coin in the less weighing is the one which is fake