Difference between revisions of "2012 AMC 8 Problems/Problem 10"
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Revision as of 16:35, 3 July 2013
Problem
How many 4-digit numbers greater than 1000 are there that use the four digits of 2012?
Solution
For this problem, all we need to do is find the amount of valid 4-digit numbers that can be made from the digits of 
, since all of the valid 4-digit number will always be greater than 
. The best way to solve this problem is by using casework.
There can be only two leading digits, namely 
or 
.
When the leading digit is , you can make 
such numbers.
When the leading digit is , you can make 
such numbers.
Summing the amounts of numbers, we find that there are 
such numbers.
See Also
| 2012 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
