Maxi Pyramid

This problem requires students to consider what happens as they try different combination of numbers at the bottom of the pyramid.  There are a lot of rules to consider when constructing the pyramid, so students need to check carefully that they have satisfied them all. When they try the extension questions they have an opportunity to practice arithmetic with positive and negative numbers.

The starting row $4,6,1,7,2$ can be used as a joint class activity to introduce the problem.  With this starting row the number at the top of the pyramid is $60$ (see Getting Started for all of the resulting numbers in the pyramid). 

Students can be challenged to make the biggest top number. 

Students could be asked what they notice about all the numbers above the bottom row - is this always true?

If the numbers on the bottom row are all positive integers, the highest possible top number may be a little under 250.

If zeroes are allowed, the highest possible top number is greater than 250.

If negative numbers are allowed it is possible to make huge top numbers...