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Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Crossing the Atlantic

Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?

On Time

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

Bell Ringing

Age 11 to 14
Challenge Level

    Suppose you are a bellringer holding a rope and you look around the church tower and see the faces of 3 friends, all about to start change ringing. To ring a 'round' each bell is rung in turn (123412341234....). The bells can be rung in any order and changing the order is known as a 'change'. As your bell goes round on its wheel you can slow it down, or speed it up, just a little but not much, so you can only change places in the ringing order with the bell just before you or just after you.

    By these rules NRICH can at first change to RNICH but not to RINCH. What are the other orders of the letters of the word NRICH that can be obtained in just one change of this sort?

    The following example shows very simple 'bell music' starting with a round and ending with a round of 4 bells, showing 8 of the 24 possible permutations, or orders.


    Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once?