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## Question

F(x) denotes the absolute difference between SOD(x) and SOD(x+2), whenever x is a positive integer.

Determine the total number of distinct values of F(x) < 2000.

Note: SOD(x) denotes the sum of digits in the base ten representation of x.

Edited by K Sengupta

## 10 answers to this question

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2 , 7 , 16 , 25

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@3ala2, there are more values of F(x)

2,7,16,25,34,.......i.e., 2, 7+9*n, n=0,1,2,....110 therefore there are 112 values of F(x)

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@3ala2, there are more values of F(x)

2,7,16,25,34,.......i.e., 2, 7+9*n, n=0,1,2,....110 therefore there are 112 values of F(x)

mm.. i agree with ur method..

F(x) can go till 2000 which means n can reach 221

then we get 223 value for F(x)

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I am so lost. Could someone please give me a quick example of F(x) in action and how it does, or does not, fit into the solution we are supposed to look for. Thanks!

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x=9;SOD(9)=9;SOD(9+2)=SOD(11)=1+1=2;f(x)=abs(9-2)=7

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mm.. i agree with ur method..

F(x) can go till 2000 which means n can reach 221

then we get 223 value for F(x)

Yaa... I thought F(x)should be less than 1000 ... thanks for verifying

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Fun puzzle. Where do you get so many puzzles, K Sengupta?

Edited by xamdam

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Fun puzzle. Where do you get so many puzzles, K Sengupta?

I was going to ask him that, xamdam. Maybe KS is a reincarnation of Ramanujan

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Fun puzzle. Where do you get so many puzzles, K Sengupta?

None of the said puzzles contributed to this site is an original.

The various sources wherefrom these problems are gleaned happens to be so numerous that I have since stopped countin' 'em.

Edited by K Sengupta

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