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Decorating With Tiles

You are decorating for spring and you’ve found a bargain. A huge box of beautifully decorated tiles, enough to provide a border in two rooms. You really can’t figure out how to arrange them. If you set a border of two tiles all around, there’s one left over. If you set three tiles all around or four or five or six there’s still one tile left over. Finally you try a block of seven tiles for each corner and you come out even. What is the smallest number of tiles you could have to get this result?

301. This is the smallest number that even divides by 7, but when divided by 2, 3, 4, 5, and 6 gives you one left over.

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