2007 Cyprus MO/Lyceum/Problem 19
Problem
120 five-digit numbers can be written with the digits . If we place these numbers in increasing order, then the position of the number is
Solution
For any number in the first slot, there are numbers, so any number starting with must greater than . After than, the rearrangement inequality gives us that are in order, but , so is the .
See also
2007 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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 • 26 • 27 • 28 • 29 • 30 |