Difference between revisions of "2005 PMWC Problems/Problem T1"
(New page: ==Problem== Call an integer "happy", if the sum of its digits is <math>10</math>. How many "happy" integers are there between <math>100</math> and <math>1000</math>? ==Solution== We hav...) |
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Revision as of 08:06, 9 October 2007
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 First question |
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 |