Difference between revisions of "1993 AIME Problems/Problem 1"
Danielguo94 (talk | contribs) (→Solution) |
|||
Line 11: | Line 11: | ||
[[Category:Intermediate Combinatorics Problems]] | [[Category:Intermediate Combinatorics Problems]] | ||
+ | {{MAA Notice}} |
Revision as of 19:25, 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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.