Difference between revisions of "1992 AIME Problems/Problem 6"
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Revision as of 19:23, 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 | |
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All AIME Problems and Solutions |
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