MathDB

1

Part of 1998 USAMO

Problems(1)

Disjoint Pairs

Source: USAMO 1998

10/9/2005
Suppose that the set {1,2,⋯ ,1998}\{1,2,\cdots, 1998\} has been partitioned into disjoint pairs {ai,bi}\{a_i,b_i\} (1≤i≤9991\leq i\leq 999) so that for all ii, ∣ai−bi∣|a_i-b_i| equals 11 or 66. Prove that the sum ∣a1−b1∣+∣a2−b2∣+⋯+∣a999−b999∣ |a_1-b_1|+|a_2-b_2|+\cdots +|a_{999}-b_{999}| ends in the digit 99.
modular arithmeticnumber theory proposednumber theory