The clock in Simpson Mall has hour, minute and second hands. Little Esu climbs onto the hour hand at 12.01 pm, and stays on it until the minute and hour hands are aligned. At that instant, Esu jumps on to the minute hand and rides on it until the hour and minute hands are aligned and then jumps on to the hour hand. In this way, Esu changes positions between the hour and minute hands whenever they are aligned. Finally, Esu jumps off the clock when all three hands are aligned.

For how many minutes in total did Esu ride the minute hand?

WIN 拢15 will be awarded to the sender of the first correct answer opened on Wednesday 4 September. The Editor鈥檚 decision is final. Please send entries to Enigma 1761, 快猫短视频, Lacon House, 84 Theobald鈥檚 Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1755 Sudoprime II: The numbers in the shaded regions are 307 and 41

The winner Alagu Meyyappan of Singapore

Jack will enter the office today at a random time between 2pm and 3pm. He will stay in the office for 15 minutes. John has a similar schedule, with the entry time chosen independently.

They have a business to transact and it requires that they are together in the office for 5 minutes before 3pm. What are the chances that the business is transacted today?

WIN 拢15 will be awarded to the sender of the first correct answer opened on Wednesday 22 December 2010. The Editor鈥檚 decision is final. Please send entries to Enigma 1622, 快猫短视频, Lacon House, 84 Theobald鈥檚 Road, London WC1X 8NS, or to enigma@newscientist.com (please include your postal address).

Answer to 1616 One good turn: Penny turned over a counter 33 times

The winner Tony McCoy O鈥橤rady of Rathfarnham, Dublin, Ireland