Sam Loyd published this puzzle in 1878. He claimed to have invented this puzzle and offered a $1,000 prize for its solution, but it's more likely he did not invent it, although the publicity surrounding the prize firmly implanted the idea in the public's mind. So much so, that many recent publications unquestioningly cite Loyd as the creator of this puzzle.
The 15-14 problem has you take a 15 block puzzle (a.k.a. sliding tile puzzle) and set it up
in its final, correct position, except that the 15 and 14 blocks
1 2 3 4
5 6 7 8
9 10 11 12
13 15 14
Now try to reach the final position by only sliding the blocks. You'll find that it is impossible. This is due to the fact that this puzzle, like Rubik's Cube, has sets of positions that are unreachable from other positions. In a 15 block puzzle, transposing any two adjacent blocks is mathematically impossible, and was proven around the time Loyd published this puzzle.