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1

Part of 1995 Mexico National Olympiad

Problems(1)

1020 handshakes between N students seated at desks in mxn array

Source: Mexican Mathematical Olympiad 1995 OMM P1

7/28/2018
NN students are seated at desks in an m×nm \times n array, where m,n≥3m, n \ge 3. Each student shakes hands with the students who are adjacent horizontally, vertically or diagonally. If there are 10201020 handshakes, what is NN?
combinatoricsnumber theoryArray