2005 PMWC Problems/Problem T1
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Problem
Call an integer "happy", if the sum of its digits is 
. How many "happy" integers are there between 
and 
?
Solution
We have a three digit integer in the form ABC. The number of happy integers per hundred is the number of positive integer solutions to 
For the one hundreds:
B+C=9: 10 solutions
two hundreds:
B+C=8: 9 solutions
so on, until there are two solutions in 9 hundreds.
See also
| 2005 PMWC (Problems) | ||
| Preceded by Problem I15 | Followed by Problem T2 | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
