It was the new year and Annabel, Belinda, Carmen and Davina went on their traditional shopping trip to the sales. "Mind you," Belinda said, "the sales are all year round now."
"True," said Davina. "But we must show some responsibility this year and limit our purchases to things that really matter."
"Like what?" asked Annabel.
"Well—uh— "
"I know!" said Carmen. "Let's all agree to buy only one bottle of perfume and spend everything else on handbags."
And so they did. It turned out that all the bottles of perfume cost the same amount. Handbags were more expensive than perfume, but they, too, all cost the same amount. All of the items cost a whole number of pounds and no goods were free.
"I spent £175," said Annabel.
"I splurged a bit," Belinda confessed. "I spent £290."
"I was very restrained," replied Carmen. "I only spent £129."
"I was even more restrained," said Davina. "I spent £60."
How much did a handbag cost?
Prospect invites you to solve the puzzle and send us the answer. Correct answers will be entered
into a draw. The winner will receive the first two volumes from the new Martin Gardner Mathematical Library, Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi and Origami,
Eleusis, and the Soma Cube (Cambridge University Press, £25 each).
Send solutions to answer@prospect-magazine.co.uk by 16th January. The winner will be announced in our February issue.
