Re: MathsBombe - observations but not the answer

In article <vp7dvm$2s8nd$1@dont-email.me>,
David Entwistle  <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

221 matched by 221.00, 0 * x^4 + 0 * x^3 + 14 * x^2 + 14 * x^1 + 11 * x^0
222 matched by 222.00, 0 * x^4 + 0 * x^3 + 14 * x^2 + 14 * x^1 + 12 * x^0
223 matched by 223.00, 0 * x^4 + 0 * x^3 + 14 * x^2 + 14 * x^1 + 13 * x^0
224 matched by 224.00, 0 * x^4 + 0 * x^3 + 14 * x^2 + 14 * x^1 + 14 * x^0

So you have correctly chosen x such that x^2 + x = 15.  Up to here we
are working in base 15 with the x^0 coins (obviously) acting as the
units column, and pairs of x^1 and x^2 coins acting as the 15s column.

To continue in base 15 beyond 224 we need a column for 15^2.  Since
x^2 + x is 15, (x^2 + x)^2 is 15^2, and is equal to x^4 + 2x^3 + x^2.
So you can get 225 by using a set of one x^4, two x^3, and one x^2
coin.

225 matched by 225.00, 1 * x^4 + 2 * x^3 + 1 * x^2 + 0 * x^1 + 0 * x^0
226 matched by 226.00, 1 * x^4 + 2 * x^3 + 1 * x^2 + 0 * x^1 + 1 * x^0
227 matched by 227.00, 1 * x^4 + 2 * x^3 + 1 * x^2 + 0 * x^1 + 2 * x^0
228 matched by 228.00, 1 * x^4 + 2 * x^3 + 1 * x^2 + 0 * x^1 + 3 * x^0
229 matched by 229.00, 1 * x^4 + 2 * x^3 + 1 * x^2 + 0 * x^1 + 4 * x^0
230 matched by 230.00, 1 * x^4 + 2 * x^3 + 1 * x^2 + 0 * x^1 + 5 * x^0

As you have presumably noticed, this works for a while, but will run
into a problem when you get to 435 = 15^2 + 14*15 which would be

   1*x^4 + 2*x^3 + 15*x^2 + 14*x^1

because now you have more than 14 of one coin.

-- Richard