A group of 7 coins consists of 5 coins of standard weight and 2 coins of lighter weight. Devise a plan to guarantee finding the two light coins using a balance scale at most three times.
1. Weigh 3 coins against 3 coins.
Result of 1 is =:
Each side contains a lowweight coin. Within each triple, weigh one against one. Unequal will result in lighter coin being declared shortweight. Equal will result in nonweighed coin being found shortweight. 3 weighings.
Result of 1 is unequal:
Low weight triplet has either one or both shortweight coins. Weigh one against one in the low weight group as weighing 2.
Weigh 2 is =:
Either both are light or both are normal. Weigh a known normal from the heavy side of weighing 1 against one of the two weighed in weighing 2. If equal, then the one not weighed in weighing 2 is one fake and the one not weighed in weighing 1 is the other. If the one from the equal pair from weighing 2 is light, then so is the other.
Weigh 2 is unequal:
The low side is a fake. Weigh the heavy side against the one unweighed in weighing 2; if they are equal, the one unweighed in weigh 1 is the second shortweight coin, otherwise the newly weighed low weight coin is the second fake.
The above presumes, as must be necessary that the lowweight coins are the same weight as each other.

Posted by Charlie
on 20151209 19:44:31 