MathDB

4

Part of 1991 Canada National Olympiad

Problems(1)

Can ten numbers be chosen so that differences be distinct?

Source: Canada National Mathematical Olympiad 1991 - Problem 4

9/29/2011
Can ten distinct numbers a1,a2,b1,b2,b3,c1,c2,d1,d2,d3a_1, a_2, b_1, b_2, b_3, c_1, c_2, d_1, d_2, d_3 be chosen from {0,1,2,…,14}\{0, 1, 2, \ldots, 14\}, so that the 1414 differences ∣a1−b1∣|a_1 - b_1|, ∣a1−b2∣|a_1 - b_2|, ∣a1−b3∣|a_1 - b_3|, ∣a2−b1∣|a_2 - b_1|, ∣a2−b2∣|a_2 - b_2|, ∣a2−b3∣|a_2 - b_3|, ∣c1−d1∣|c_1 - d_1|, ∣c1−d2∣|c_1 - d_2|, ∣c1−d3∣|c_1 - d_3|, ∣c2−d1∣|c_2 - d_1|, ∣c2−d2∣|c_2 - d_2|, ∣c2−d3∣|c_2 - d_3|, ∣a1−c1∣|a_1 - c_1|, and ∣a2−c2∣|a_2 - c_2| are all distinct?
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