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

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Discussion Overview

The discussion revolves around the mathematical problem of finding the sum of two three-digit numbers, $abc$ and $cba$, derived from the expression $pqr - rqp$ under the conditions that $p \ge r + 2$. The focus is on exploring the implications of these conditions and the relationships between the digits.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Participants discuss the formulation of the problem involving the three-digit number $pqr$ and the condition $p \ge r + 2$.
  • There are multiple requests for clarification regarding whether the problem has been posted previously, indicating uncertainty about its originality.
  • Some participants express a desire to find previous discussions or solutions related to this problem.
  • One participant mentions a specific link and property related to three-digit numbers, suggesting a potential avenue for exploration.

Areas of Agreement / Disagreement

There is no consensus on the originality of the problem, as participants express differing views on whether it has been posted before. The mathematical aspects of the problem remain under discussion without a clear resolution.

Contextual Notes

Participants have not reached a conclusion regarding the solution to the problem, and there are unresolved questions about the previous existence of similar problems.

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

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

Find $abc+cba$.

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
 
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.
 
anemone said:
...
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)
 
MarkFL said:
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
 
kaliprasad said:
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! :o
 
kaliprasad said:
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
 

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