Sam displays cans in 3 triangular stacks. With the same number he
could make one large triangular stack or stack them all in a square
based pyramid. How many cans are there how were they arranged?
Here is a collection of puzzles about Sam's shop sent in by club
members. Perhaps you can make up more puzzles, find formulas or
find general methods.
Investigate polygons with all the vertices on the lattice points of
a grid. For each polygon, work out the area A, the number B of
points on the boundary and the number of points (I) inside the
polygon. Can you find a formula connecting A, B and I?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.