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Shown here are 7 matchsticks placed in such a way that it forms a horizontal row (matchsticks 2,4,6), two vertical rows (matchsticks 1,2,3 and 5,6,7) and two diagonal rows (matchsticks 1,4,7 and 3,4,5) Note the 3 matchsticks in a row each time. The vertical and horizontal distance between matchsticks is exactly one matchstick.
The challenge is to add 2 matchsticks so that there are 6 diagonal rows, 3 vertical rows and 1 horizontal row, still with 3 matchsticks in a row.
Another solution, in which diagonals are assumed to have the same angle as shown in the original diagram, is to place one stick X exactly on top of stick 3 and another stick Y further along the diagonal of (1, 4, 7). X adds one vertical row and one diagonal, and Y adds (1, 4, Y), (1, 7, Y) and (4, 7, Y) resulting in three more diagonal triads. Perhaps this can be added as a new stick puzzle, with the added instruction that all diagonals must be at 45 degree inclines.
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