Edmund's Brainteasers
Problem 3
Problem 3: The bowing singers
Before Christmas some members of the choir decided to perform Christmas carols in the Church Hall. Twice as many girls sang as boys. In keeping with the season of goodwill, they decided to be extra courteous and when the boys came onto the stage, each bowed to every other boy. Then the girls came on stage and each bowed to every other girl. Next each boy bowed to each girl, then each girl bowed to each boy. Finally each performer bowed to the audience. Edmund, who was in the audience and greatly enjoyed the occasion, counted 144 bows. How many boys sang the carols? The performance was so popular that they repeated it on the following night. The same number of girls sang, but one additional boy joined the singers. How may bows were there on this second night.