Starting in the top left corner of a 2×2 grid, there are 6 routes (without backtracking) to the bottom right corner.

2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

>>In the 20×20 grid below, four numbers along a diagonal line have been marked in red.