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.
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten.
Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it works?
Investigate polygons, like those in the diagrams, with all the
vertices on the lattice points of a grid. For each polygon, work
out the area A, count the number B of grid points on the boundary,
and count the number I of grid points in the interior of the
polygon. Can you find a formula connecting A, B and I? Display your
results in a table, for example:
The following method may help you to find a formula if you do
not spot the pattern. First divide your polygon into triangles each
of which has an area of one half a square unit. Next consider the
total sum of all the angles in all the triangles in two different
ways. If you assume that any polygon can be split into triangles in
this way, then this method gives a proof of a general formula
connecting A, B and I.