Help with Math Olympiad question pls.

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Help with Math Olympiad question pls.

Postby turquoise » Mon May 31, 2010 11:26 am

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

Thanks.

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Postby turquoise » Mon May 31, 2010 5:00 pm

No one's able to solve this question?

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Postby verykiasu2010 » Mon May 31, 2010 11:45 pm

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


17
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Re: Help with Math Olympiad question pls.

Postby mjl » Tue Jun 01, 2010 9:24 am

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.

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Postby Vanilla Cake » Tue Jun 01, 2010 9:30 am

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

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Postby verykiasu2010 » Tue Jun 01, 2010 11:16 am

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
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