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Kakuro

Write a digit from 1 through 9 in every box. A number above a diagonal line indicates the sum of the digits in the white boxes immediately to its right. A number below a diagonal line indicates the sum of the digits in the white boxes directly below it. Within a consecutive horizontal or vertical sequence of white boxes, no digit occurs more than once.

Example

When solving puzzles of this kind, often it pays off to find the right place to start from. We might, for example, choose the number 12, which spans three boxes, immediately we are confronted with a quite large number of possibilities without any benefits as we will soon discover. Instead we will consider the 4 that points downwards in the upper right of the diagram. There are only two ways to fill in the corresponding boxes, (1,3) and (3,1). Note that (2,2) is invalid, because the 2 occurs more than once there. If we now also look at the horizontal 6, it becomes apparent that the (3,1) we had in mind does not suffice, because it would force the 6 to become (3,3). So (1,3) must be correct.

Now it is also clear that 6 = (5,1) and that we should read the vertical 22 now as a 17 divided over two boxes without using another 5. A little bit of calculation shows us that the only two possibilities to make 17 with just two digits are (8,9) and (9,8). At this point there are two different options which lead to the conclusion that (8,9) is the correct answer. For the first option, look what happens if 9 were added to the 3 that needs to make 12 divided over three boxes, it asks for a 0, but that is not valid. For the second option, imagine the 8 at the bottom, where it is also part of the horizontal 16 divided over two squares. This will result in (8,8). The remaining squares can be filled more easily.

Background

This genre was invented by Dell Magazines. Michael Rios was the first to make use of 2x2 squares, in his puzzle for the USPC 2008.


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