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What are the missing numbers in the pyramids?

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Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.

You Owe Me Five Farthings, Say the Bells of St Martin's

Age 11 to 14 Challenge Level:

Click on 'Start' in the interactivity below to listen to the pattern from Oranges and Lemons played on four bells. You can watch the numbers light up on the diagram to help you listen.

Now it's your turn to ring one of the bells!
Press '1' on your keyboard to choose bell 1 and click on 'Start'.
In the first line your bell will be played for you, so come in on the second line by pressing '1' again to ring the bell. Remembering the path from Oranges and Lemons should help you.

When you've got the hang of bell 1, try the other bells, using '2', '3' and '4' on your keyboard. Do you need to learn new paths for these?

Explain how you know when it is your turn to ring.

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This is the second of three related problems. The first is Oranges and Lemons, Say the Bells of St Clement's , and the third is When Will You Pay Me? Say the Bells of Old Bailey .