Pyramids

What are the missing numbers in the pyramids?

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?

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.

When Will You Pay Me? Say the Bells of Old Bailey

Stage: 3 Challenge Level:

This problem is the third of three related problems. The first problem is Oranges and Lemons, Say the Bells of St Clement's , and the second is You Owe Me Five Farthings, Say the Bells of St Martin's .

When bellringers ring handbells (as opposed to bells in a church tower), they often use two bells each. If you've mastered ringing one bell, now is your chance to try ringing two!

Click on 'Start' in the interactivities below to listen to four, six and eight bells. You can watch the numbers light up on the diagrams to help you listen.

Now it's your turn to ring two of the bells!

Press '1' or '2' on your keyboard to choose bells 1 and 2 and click on 'Start'.
In the first line your bells will be played for you, so come in on the second line.

To make it realistic, control the higher bell (the smaller one) with your left hand and the other with your right hand.

Look at the diagram very carefully. Can you see how to remember the paths made by bells 1 and 2?
Make sure that you ring them the right way round!

When you can ring bells 1 and 2, try ringing bells 3 and 4. Do you need to learn any new paths?

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Now try ringing bells 1 and 2 when there are six bells. Do you need to learn a new pattern?
What about when you ring bells 3 and 4, or bells 5 and 6?

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Now try ringing two of these 8 bells.

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Explain how to work out when you should ring your bells.