## Help with Math Olympiad question pls.

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### Help with Math Olympiad question pls.

Find the number of integers in the set {1,2,3, ...., 2009} whose sum of the digits is 11.

Thanks.

turquoise
BrownBelt

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No one's able to solve this question?

turquoise
BrownBelt

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turquoise wrote:No one's able to solve this question?

17
verykiasu2010
KiasuGrandMaster

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### Re: Help with Math Olympiad question pls.

turquoise wrote:Find the number of integers in the set {1,2,3, ...., 2009} whose sum of the digits is 11.
Thanks.

I think there is no simple way, you have to use the brute force method.
29...92 (8)
119..191 (9)

209..290 (10)
308..380 (9)
407..470 (8)
:
:
902..920 (3)

1019..1091 (9)

1109..1190 (10)
1208..1280 (9)
1307..1370 (8)
:
:
1901,1910 (2)
2009 (1)

total=8+9+(3+4+...+10)+9+(1+2+..+10)
=26+ ((3+10)/2) x8 + ((1+10)/2)x10
=133
Last edited by mjl on Tue Jun 01, 2010 9:33 am, edited 1 time in total.

mjl
BlueBelt

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verykiasu2010 wrote:
turquoise wrote:No one's able to solve this question?
17

Hi verykiasu2010,
This is a 1-mark question (Q24) from Singapore Mathematical Olympiad (SMO) 2009 - Junior Section held on Tuesday, 2 June 2009 from 0930 - 1200 hrs.

The answer is 133 and the solution is also published. As the solution has subscript and superscript characters, it's not possible for me to type out the given solution for your review.The method used to solve is using combinatorics to find out the 3 sets of integers that satisfies the property.From 0001~0999 - 69 number of solutions, 1001 ~ 1999 - 63 number of solutions and 2001 ~ 2009 - 1 solution. 69+63+1=133.

Submitted by VC's mum

Vanilla Cake
BlackBelt

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Vanilla Cake wrote:
verykiasu2010 wrote:
turquoise wrote:No one's able to solve this question?
17

Hi verykiasu2010,
This is a 1-mark question (Q24) from Singapore Mathematical Olympiad (SMO) 2009 - Junior Section held on Tuesday, 2 June 2009 from 0930 - 1200 hrs.

The answer is 133 and the solution is also published. As the solution has subscript and superscript characters, it's not possible for me to type out the given solution for your review.The method used to solve is using combinatorics to find out the 3 sets of integers that satisfies the property.From 0001~0999 - 69 number of solutions, 1001 ~ 1999 - 63 number of solutions and 2001 ~ 2009 - 1 solution. 69+63+1=133.

Submitted by VC's mum

Thank you very much !
verykiasu2010
KiasuGrandMaster

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