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Mathematics

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A + B + C = 13

Starting from the top and going horizontally the missing numbers are:
18, 3, 1, 9, 7, 6, 2, 8, 16, 4, 15, 10

The sum of 1+2+3+...+18+19 = 190
There are 5 vertical lines (3,4,5,4,3 in each) so each line has to add to 190 / 5 = 38

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