1992 AIME Problems/Problem 6
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) | ||
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Followed by Problem 7 | |
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