2012 AMC 8 Problems/Problem 10
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 | |
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