Edmund's Brainteasers
Problem 8
Solution
Problem 8: Weighing candles. Solution
Suppose first that there were 81 candles in the box. Divide them into three batches of 27 each and weigh one batch against a second batch. If one of these two batches contains the lighter candle we find out. If the batches are of equal weight, the light candle is in the third batch. Take the batch of 27 containing the lighter candle and divide it into 3 batches of 9. Again weighing one batch against a second allows us to determine which batch of nine contains the lighter candle. So far two weighings have been done. A third weighing determines which of 3 batches of 3 candles contains the light one and the fourth and final weighing finds the light candle. But we only have 80 candles, not 81. Easy - start with 2 batches of 27 and one of 26. If the light candle is in one of the batches of 27 proceed as before. If it is in the batch of 26 add one candle from one of the batches of 27 good candles and proceed as before. In all cases we have solved it with 4 weighings.