Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Label this plum tree graph to make it totally magic!
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
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 .