What are the missing numbers in the pyramids?
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.
We received good solutions from Gareth, Ed and
Omer from Dartford Grammar School, Harry from Culford School and
Alex, Alice, George, Nell and Tom from Gorseland School. Thank you
Harry explained how he knows when it is his
turn to ring:
Alex, Alice, George, Nell and Tom from
Gorseland School sent the following explanation:
Ken, a volunteer (and bellringer) helping at
their school wrote:
We are delighted you enjoyed the problem.