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© Copyright 2002, Jim Loy
Number Place is a Dell puzzle, which is usually easy, and
occasionally very difficult. Digits 1 through 9 go in each small square (see
the diagram on the left, which I designed). Furthermore, the puzzle is divided
into nine medium sized boxes (with the dark borders in the diagram), each of
which will contain (once the puzzle is solved) the digits 1 through 9. And each
row and column of the entire puzzle will have the digits 1 through 9 in it.
Although numbers are used, these puzzles have nothing to do with arithmetic. Any nine symbols would work. Sometimes Dell uses letters.
This puzzle (above left) is a moderately difficult one of my own. In the top row, we need a 1. It cannot be in the left box of nine digits, as there is already a 1 there. And it cannot be in the middle box. So there is only one place where it can be, to the left of the 9 and 8 in the upper right box, easy. Other 1s cannot be positioned just yet, and so we go on to 2. We could go through the digits in any order, but starting with 1 and ending with 9 is the most obvious order. Dell knows that, so maybe we should start with 9? Once we have gone through all nine digits, we can either go through them again, or concentrate on individual boxes of nine digits, as some of those now probably have solvable squares, now that some of the missing digits have been positioned.
Usually that is all you have to do to solve a number place. But in the more difficult ones, you will have to do something more complicated, a kind of combination of guesses of digits and/or squares. You can tentatively place a number or two in two or three squares (mentally or in pencil perhaps) in a row or column or box. This may help you place other numbers of that same row, column, or box, or into other rows, columns, or boxes. For example, in a column, if we have three remaining empty squares which can only be 1, 2, and 3 in some order, but two of them must be 1 or 2 in some order, then we deduce that the third one must be 3. It is the same process that we used with simpler puzzles, two of three squares can't be 3, but here we eliminated 3 in a slightly more indirect way. We can do the same in even more complicated situations. And this may take extra sheets of paper, in order to list all of the possible permutations.
In the above diagram, about half of the puzzle can be solved simply, merely by trying the digits 1 through 9 in different places, in some systematic ways. Then a few (three or four) multiple digit or square combinations (as described in the previous paragraph) must be attempted. Then the rest of the puzzle becomes simple to complete.
Addendum:
Here is a difficult number place, which I designed (I
took an easy one, and deleted numbers until it was difficult).
Click here for the solutions to both puzzles.