Difference between revisions of "1986 AIME Problems/Problem 6"
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== See also == | == See also == | ||
{{AIME box|year=1986|num-b=5|num-a=7}} | {{AIME box|year=1986|num-b=5|num-a=7}} | ||
| + | * [[AIME Problems and Solutions]] | ||
| + | * [[American Invitational Mathematics Examination]] | ||
| + | * [[Mathematics competition resources]] | ||
[[Category:Intermediate Number Theory Problems]] | [[Category:Intermediate Number Theory Problems]] | ||
Revision as of 13:48, 6 May 2007
Problem
The pages of a book are numbered 
through 
. When the page numbers of the book were added, one of the page numbers was mistakenly added twice, resulting in an incorrect sum of 
. What was the number of the page that was added twice?
Solution
Denote the page number as 
, with 
. The sum formula shows that 
. Since cannot be very large, disregard it for now and solve 
. The positive root for 
. Quickly testing, we find that 
is too large, but if we plug in 
we find that 
, our solution.
See also
| 1986 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
