You are decorating for spring, and you've found a bargain: a huge box of beautiful decorated tiles, enough to provide a border in two rooms. You really can't figure out how to arrange them, however. 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?

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THE SOLUTION

There are 301 tiles. This is the smallest number that will give you a remainder of 1 when divided by 2, 3, 4, 5, and 6, but divided by 7 leaves nothing over.