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Man Food

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?

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Sam Again

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.

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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?

Simultaneous Multiplying

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2


From the three equations we see that $(abc)^2=2\times 24\times 3=144$ and so, since $abc$ is positive, $abc=12$. Then the third equation tells us that $a=1/2$, the second that $b=4$ and the first that $c=6$. Therefore $a+b+c=10\frac{1}{2}$.

This problem is taken from the UKMT Mathematical Challenges.
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