Solve for $abc+cba$ with $pqr$, $p\ge r+2$, and $pqr-rqp=abc$

[anemone]

Let $pqr$ be a three digit number in base 10, with $p\ge r+2$ and $pqr-rqp=abc$.

Find $abc+cba$.

 

[kaliprasad]

Let $pqr$ be a three digit number in base 10, with $p\ge r+2$ and $pqr-rqp=abc$.

Find $abc+cba$.

Spoiler

1089

as differnce is a multilple of 9 and also 11 so of 99

99*n when digits reversed gives 99 *(11 -n) and so sum = 99 * 11 or 1089

 

[anemone]

Thanks kaliprasad for your great solution!:)

Now that I re-read this problem, I was wondering if I have posted it in the past at MHB. I felt I did and so I tried to find such similar problem but I couldn't find any. I am sorry if anyone has read this problem before because my memory failed me when I have posted many a challenge problems here in last two years or so.

 

[MarkFL]

...
Now that I re-read this problem, I was wondering if I have posted it in the past at MHB. I felt I did and so I tried to find such similar problem but I couldn't find any. I am sorry if anyone has read this problem before because my memory failed me when I have posted many a challenge problems here in last two years or so.

I did a search and did not find that you have previously posted this problem. But, given the sheer volume of problems you have posted, I doubt anyone would fault you for it. And if they do, send them to my office...(Punch) (Tongueout)

 

[kaliprasad]

I did a search and did not find that you have previously posted this problem. But, given the sheer volume of problems you have posted, I doubt anyone would fault you for it. And if they do, send them to my office...(Punch) (Tongueout)

I have not seen the problem. I would like a link to the previous solution post

 

[anemone]

I would like a link to the previous solution post

I will refer it to you if I really did post such similar problem before at our site and that I found it, don't worry, kali!

 

[MarkFL]

I have not seen the problem. I would like a link to the previous solution post

I didn't find that it was previously posted. :D

 

[kaliprasad]

the link 1089 and a Property of 3-digit Numbers is interesting