Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
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?
Can you adapt your insights so that they apply to pyramids with different sequences on the bottom layer?
What if the numbers on the bottom layer go up in 2s? Or 3s? Or start at 17 and go up in 7s? Or...
This spreadsheet might be useful for exploring such pyramids with four or five layers.
You could adapt it to work on even larger pyramids.
This problem features in Maths Trails - Generalising, one of the books in the Maths Trails series written by members of the NRICH Team and published by Cambridge University Press. For more details, please see our publications page .