### 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:

You might find it useful to count "1, 2, 3, 4" to yourself during each row, emphasising the number on which you are going to ring. So if you are ringing bells 1 and 2, you might say

" 1 , 2 , 3, 4,
1 , 2 , 3, 4,
1 , 2, 3 , 4,
1, 2 , 3, 4 ",
etc.

Try to remember in which position you are going to ring on the current row whilst working out in which position you will ring on the next row, using the path to help you work it out.

Don't try to remember the lines of numbers: it's too confusing!

If you remember that you are ringing in positions 1 and 2 on one row, don't think of the positions on the next row as 2 and 1 (or you'll forget to ring in position 1!). Instead, think of ringing in positions 1 and 2 but the other way round (that is, with the bells in the other order). Then you'll remember which bell has to go first.