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Problem Description
In the grid shown, the digits 19 are arranged so that the first row added to the second row equals the bottom row  583+146=729.
Now if the grid is rotated clockwise through 90 degrees, you will see that the first two rows still add up to the last row  715+248=963.
Can you find another combination of the digits 19 which has the same property? J. J. Clessa. Problem # 64 Background & TechniquesHere's another program that uses the permutation algorithms developed in Permutes1 (the first programs was Alphametics). We'll generate all possible permutations of the numerals 19 and, for each, check to see if the conditions are met. Remember there are 9! (9x8x7...x2x1) permutations of 9 things taken 9 at a time, so we only have about 360,000 to check. We must convert the three integers to a single number before testing. We can do this by multiplying the first digit (the thousands position) by 1000, adding it to 100 times the 2nd digit and then adding the rightmost digit. To find a solution, we'll have to do this for the numbers represented by the 3 rows and the 3 columns. There is one more perhaps new coding technique here; A stringgrid is used to display the result. One of the features of a stringgrid is that the user can select a cell to trigger some action, even though we're not doing that here. However the currently selected sell (by default the first cell) is highlighted to show that it's selected. To uncolor this cell I used a DrawCell exit called each time a cell is displayed. The exit simply clears the cell and writes the digit. Running/Exploring the Program
Suggestions for Further ExplorationsI'll be back when I think of something. Rotate counterclockwise?

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