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 low-weight coin. Within each triple, weigh one against one. Unequal will result in lighter coin being declared shortweight. Equal will result in non-weighed 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 low-weight coins are the same weight as each other.
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Posted by Charlie
on 2015-12-09 19:44:31 |
solution