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Determine the number of n-tuples of integers

Source: India tst 2002 p6

July 13, 2012

linear algebramatrixcombinatorics unsolvedcombinatorics

Problem Statement

Determine the number of

n

-tuples of integers

(x_1,x_2,\cdots ,x_n)

such that

|x_i| \le 10

for each

1\le i \le n

and

|x_i-x_j| \le 10

for

1 \le i,j \le n