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 correct solutions from Alex,
Alice, George, Nell and Tom from Gorseland School, Oliver, Edward,
Alex and Paul from Dartford Grammar School, Katie from Bathurst
West PS, Adam, Annie, Vijay, Louise, Jude, Aaron and Mary from St.
Mary Star of The Sea, Ben from Victoria College, Bethany, Alicia
and Grace from Willaston Primary School, Samantha and Frances from
St. Alban's Catholic Primary School and Max and William from
Brenchley and Matfield School. Well done to you all.
Alex, Alice, George, Nell and Tom sent in this diagram showing the
paths of the six bells:
The pattern of the paths for eight bells was
sent by Edward:
Max and William also sent us a solution for
They even tried to find a solution for fifteen
bells, but because it is an odd number of bells they weren't able
to stick to the rule that on alternate rows we swap all of the
bells (in pairs) and on the remaining rows, we fix the bells on
either end and swap the rest.