Home > Mathematica, Mathematics > Climbing the lattice

Climbing the lattice

I have seen a lot of references to Sylvester’s stamp puzzle or problem. Here is a statement and it’s solution.

Fundamentally, it illustrates a property of relatively prime numbers.

For, p,q relatively prime numbers, there exist a, b \in \mathbf{Z} such that:

a p +b q =1. Consequently, any integer can by choosing suitable a, b. The problem constrains the solutions to the first octant. There are is a maximum integer that has no solution in this octant: pq -p-q.

If there stamp denominations are not relatively prime then there are an infinite number of ‘gaps’, hence no finite maximum.

The CDF here is motivated by this puzzle (for denominations 4 and 7).

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Categories: Mathematica, Mathematics
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