Diagonal Touch!
Number Theory
Level
3
How many boxes are crossed by a diagonal in a rectangular table formed by 463 × 310 squares?
The answer is 772.
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Without loss of generality, we can assune that the diagonal starts from the top left square and goes till the lower right square. Let us mark every square through which diagonal passes to be X. In every row, mark the square nearest to left side of the table with letter A. Similarly, in each column, we mark the square nearest to the upper side with letter B. We can say that every X is marked at least once, and the top left square is markerd twice. Thus, total number of X = 463 + 310 - 1 = 772