Difference between revisions of "1993 AIME Problems/Problem 1"
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Revision as of 18:25, 4 July 2013
Problem
How many even integers between 4000 and 7000 have four different digits?
Solution
The thousands digit is 
. If the thousands digit is even (
, 2 possibilities), then there are only 
possibilities for the units digit. This leaves 
possible digits for the hundreds and 
for the tens places, yielding a total of 
.
If the thousands digit is odd (
, one possibility), then there are choices for the units digit, with digits for the hundreds and for the tens place. This gives 
possibilities. Together, the solution is 
.
See also
| 1993 AIME (Problems • Answer Key • Resources) | ||
| Preceded by First question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
