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

  • Thread starter Thread starter anemone
  • Start date Start date
AI Thread Summary
The discussion revolves around solving the equation $abc+cba$ derived from the three-digit number $pqr$, where $p \ge r + 2$ and $pqr - rqp = abc$. Participants express uncertainty about whether the problem has been posted before, with one member confirming they could not find a previous instance. The conversation includes light-hearted remarks about the volume of problems shared in the forum. Additionally, there is mention of an interesting link related to three-digit numbers. The focus remains on finding the solution to the mathematical problem presented.
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Let $pqr$ be a three digit number in base 10, with $p\ge r+2$ and $pqr-rqp=abc$.

Find $abc+cba$.
 
Mathematics news on Phys.org
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
 

Similar threads

MHB Show that there are points Q,R on C such that the triangle PQR is equilateral.
Replies
1
Views
1K
MHB *8s6.12.7 Find the lengths of the ides of the triangle PQR
Replies
2
Views
1K
MHB Triangle $PQR$: Find $\tan P,\,\tan Q,\,\tan R$ Values
Replies
4
Views
2K
MHB Solve for $\overline{abc}:$ $N=3194$
Replies
3
Views
1K
MHB Solve the triangle PQR by finding their angles
Replies
2
Views
2K
MHB Finite Group Inverses: Proving $N_{ABC}=N_{CBA}$
Replies
1
Views
1K
MHB What is the perimeter of triangle ABC?
Replies
2
Views
5K
MHB System of Equations: Find Real Numbers $p,q,r,s$
Replies
1
Views
1K
MHB Finding $\angle PCA$ in Triangle ABC with $\angle ANB = 90^\circ$
Replies
13
Views
4K
MHB Is there a formula for finding the perimeter of a triangle with known vertices?
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top