6

Part of 1993 Iran MO (3rd Round)

Problems(1)

Prove that number of numbers t in I is less than 1000

Source: Iran Third Round Problems 1993 – Poblem 6

x_1, x_2, \ldots, x_{12}

be twelve real numbers such that for each

1 \leq i \leq 12

|x_i| \geq 1

I=[a,b]

be an interval such that

b-a \leq 2

. Prove that number of the numbers of the form

t= \sum_{i=1}^{12} r_ix_i

r_i=\pm 1

, which lie inside the interval

I

1000

algebra proposedalgebra