1990 AJHSME Problems/Problem 12
From AoPSWiki
Problem
There are twenty-four 
-digit numbers that use each of the four digits 
, , 
, and 
exactly once. Listed in numerical order from smallest to largest, the number in the 
position in the list is
Solution
For each choice of the thousands digit, there are 
numbers with that as the thousands digit. Thus, the six smallest are in the two thousands, the next six are in the four thousands, and then we need more numbers.
We can just list from here: 
.
See Also
| 1990 AJHSME (Problems • Resources) | ||
| Preceded by Problem 11 | Followed by Problem 13 | |
| 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 | ||
