Difference between revisions of "2005 PMWC Problems/Problem T1"

Latest revision as of 08:07, 9 October 2007

Call an integer "happy", if the sum of its digits is $10$ . How many "happy" integers are there between $100$ and $1000$ ?

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 $B+C=10-A$

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.

$10+9+8\cdots+2=54$

Revision as of 08:05, 9 October 2007 (view source) 1=2 (talk \| contribs) (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...)		Latest revision as of 08:07, 9 October 2007 (view source) 1=2 (talk \| contribs) (→‎See also)
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	==See also==		==See also==
		+	{{PMWC box\|year=2005\|num-b=I15\|num-a=T2}}