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September 2007 Solution
The Tower of Pascal has 19 floors.
The floors can be traversed in the following order:
1, 9, 17, 6, 14, 3, 11, 19, 8, 16, 5, 13, 2, 10, 18, 7, 15, 4, 12, 1
If there were one fewer floors (i.e. 18), then it would be impossible to get to floor 8. One certainly cannot get to floor 8 from below as they would have to come from floor 0 which is not available. Thus to get to floor 8 one must come from above, leaving from floor 19.
In addition, if there were only 18 floors, then it would be impossible to leave floor 11. Going down would be impossible, since there are only 10 floors below floor 11. Going up would also be impossible with 18 floors because going up 8 floors from floor 11 would require a 19th floor.
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