# Difference between revisions of "1998 USAMO Problems/Problem 1"

(moved 1998 USAMO Problems/Problem 1 to 1998 USAMO Problems/Problem 3: Wrong problem, I fix'd it) |
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− | + | == Problem == | |

+ | Suppose that the set <math>\{1,2,\cdots, 1998\}</math> has been partitioned into disjoint pairs <math>\{a_i,b_i\}</math> (<math>1\leq i\leq 999</math>) so that for all <math>i</math>, <math>|a_i-b_i|</math> equals <math>1</math> or <math>6</math>. Prove that the sum <cmath> |a_1-b_1|+|a_2-b_2|+\cdots +|a_{999}-b_{999}| </cmath> ends in the digit <math>9</math>. | ||

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+ | == Solution == | ||

+ | {{solution}} |

## Revision as of 11:55, 16 April 2011

## Problem

Suppose that the set has been partitioned into disjoint pairs () so that for all , equals or . Prove that the sum ends in the digit .

## Solution

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*