The ability to simplify means to eliminate the unnecessary so that the necessary may speak.
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I did it in perl - and not terribly efficiently. Generated the primes up to 30,000,000 because that's about all that the simple sieve code I found would do in the 4Gb of memory I had available, figured it was probably enough.
And keeping ALL the lists in memory as both arrays and hashes was actually not too bad - wrote it in about 10 minutes and it took another 5 to run. Woot.
My first-pass recursive attempt at the robots thing was totally intractable, and the second time when I forgot to "use bigint" I actually submitted the wrong number through doing insufficient checking (oh the embarassment) - but once you figure that: value(N, M) == value(N - 1, M) + value (N, M - 1) and value (1, x) == value (y, 1) == 1, then it's pretty trivial to just build an N x M array and calculate the values.
It is nice having a multi-core modern machine with 4Gb of ram for the prime problem though - it makes brute force much cheaper, and coming up with a good algorithm for a once-off computation rather worthless.
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