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

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In summary: I think it is a good related reference.In summary, the conversation discusses a problem involving a three digit number in base 10, with certain conditions for its digits. The challenge is to find the sum of a specific permutation of the digits. The poster apologizes if this problem has been posted before, but a search did not yield any previous results. A related link on the topic is also provided for further reference.
  • #1
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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  • #2
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
 
  • #3
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.
 
  • #4
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)
 
  • #5
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
 
  • #6
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! :eek:
 
  • #7
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
 
  • #8

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

What is the equation to solve for $abc+cba$?

The equation to solve for $abc+cba$ is $pqr-rqp=abc$. This equation is derived from the given information that $p\ge r+2$ and $pqr-rqp=abc$.

What is the relationship between $p$, $q$, and $r$?

The relationship between $p$, $q$, and $r$ is that they are all variables in the equation $pqr-rqp=abc$. $p$, $q$, and $r$ are also related by the condition $p\ge r+2$.

How does the condition $p\ge r+2$ impact the equation?

The condition $p\ge r+2$ is important because it determines the range of possible values for $p$ and $r$. This condition ensures that $p$ is always greater than or equal to $r+2$, which in turn affects the value of $q$.

Can the equation $pqr-rqp=abc$ be solved for any values of $p$, $q$, and $r$?

No, the equation $pqr-rqp=abc$ cannot be solved for any values of $p$, $q$, and $r$. The equation is dependent on the condition $p\ge r+2$, and if this condition is not met, the equation cannot be solved.

What is the significance of solving for $abc+cba$ with $pqr$, $p\ge r+2$, and $pqr-rqp=abc$?

Solving for $abc+cba$ with $pqr$, $p\ge r+2$, and $pqr-rqp=abc$ allows us to find the numerical value of this expression in terms of the variables $p$, $q$, and $r$. This can be useful in various applications of mathematics and science, such as in solving equations or analyzing data.

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