10 replies to this topic

[K Sengupta]

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, 30 October 2009 - 11:21 PM.

[3ala2]

Spoiler for i think

2 , 7 , 16 , 25

[adee]

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

Spoiler for

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

[3ala2]

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

Spoiler for

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..

Spoiler for but i think ur answer is wrong

F(x) can go till 2000 which means n can reach 221
then we get 223 value for F(x)

[Tuckleton]

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!

[plainglazed]

Spoiler for Tuck

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

[adee]

mm.. i agree with ur method..

Spoiler for but i think ur answer is wrong

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

[xamdam]

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

Edited by xamdam, 31 October 2009 - 10:40 PM.

[jerbil]

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

[K Sengupta]

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, 01 November 2009 - 03:46 PM.