Difference between revisions of "1992 AIME Problems/Problem 6"
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[[Category:Intermediate Number Theory Problems]] | [[Category:Intermediate Number Theory Problems]] | ||
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Revision as of 18:23, 4 July 2013
Problem
For how many pairs of consecutive integers in 
is no carrying required when the two integers are added?
Solution
Consider what carrying means: If carrying is needed to add two numbers with digits 
and 
, then 
or 
or 
. 6. Consider 
. 
has no carry if 
. This gives 
possible solutions.
With 
, there obviously must be a carry. Consider 
. have no carry. This gives 
possible solutions. Considering 
, 
have no carry. Thus, the solution is 
.
| 1992 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 | ||
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