Edmund's Brainteasers
Problem 3
Solution
Problem 3: The bowing singers. Solution.
Each singer bowed to every other. Of course they didn't bow to themselves but they did bow to the audience. Hence each singer bowed the exact number of times that there were singers. There must therefore have been 12 singers each bowing 12 times to give 144 bows. As there were twice as many girls as boys, there were 4 boys and 8 girls. On the next night there were 13 singers, so there must have been 13 bows from each of 13 singers making a total of 169 bows.