Help with Math Olympiad question pls.

[turquoise]

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


Thanks.

[turquoise]

No one’s able to solve this question?

[verykiasu2010]

turquoise:

No one's able to solve this question?

17

[mjl]

turquoise:

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

[Vanilla Cake]

verykiasu2010:

turquoise:

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

[verykiasu2010]

Vanilla Cake:

verykiasu2010:

[quote=\"turquoise\"]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[/quote]Thank you very much !