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 10:55, 16 April 2011
Problem
Suppose that the set 
has been partitioned into disjoint pairs 
(
) so that for all 
, 
equals 
or 
. Prove that the sum ![\[|a_1-b_1|+|a_2-b_2|+\cdots +|a_{999}-b_{999}|\]](http://latex.artofproblemsolving.com/c/9/8/c986d59da1a579f6d783633ebe60315bc9ede782.png)
ends in the digit 
.
Solution
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