Mod-Seven Multiplication Puzzle
If you're unfamiliar with the term 'modulo seven' don't let the title scare you. You only need to be able to multiply and divide to solve this next puzzle. Place the numbers 1, 2, 3, 4, 5, and 6 so that each appears exactly once in each row and each column. The clues in each cage represent the product of the entries in the cells of that cage modulo seven. To phrase that differently, this means the clues give the remainder of the product of those entries when divided by seven. For example, a clue of 1 means the product is either 1, 8, 15, 22, 29, ... and a clue of 4 means the product is 4, 11, 18, 25, 32, ... and so on. Of course, since no product of the numbers from 1 to 6 can give you numbers like 11 or 29, there are not that many possibilities.
Some of you who know about finite groups, or just are observant, may realize this puzzle is mathematically equivalent to an addition puzzle modulo six if you switch the clues correctly. Thus you can solve either this either with multiplication or addition. You may find that the multiplication puzzle feels different, or you may not. It's all good.
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