Correct in every respect Pondy

- Joined
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S.Yorks.England- Joined
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S.Yorks.England- Joined
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Wherever@venda

"The equation 81-34=47 is true but the reverse equation 74--43 =18"*said*

Thankfully, we seem to have gone off the 700 kick:-

The equation 81-34=47 is true but the reverse equation 74--43 =18 is not true**Find an example of such an equation using three 2 digit numbers and involving a subtraction which is true in both directions -or prove there isn't one.**

Is that supposed to be only one minus [-] sign in front of the 43?- Joined
- 18 Apr '10
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S.Yorks.England@bigdogg

Yes*said*

"The equation 81-34=47 is true but the reverse equation 74--43 =18"

Is that supposed to be only one minus [-] sign in front of the 43?

The equation must be in the format x-y =z- Joined
- 22 Apr '05
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Linkenheim@venda

There is no pair that it works for. I can't stringently prove it beyond showing that it won't work for any combination of the second digits...*said*

Thankfully, we seem to have gone off the 700 kick:-

The equation 81-34=47 is true but the reverse equation 74--43 =18 is not true**Find an example of such an equation using three 2 digit numbers and involving a subtraction which is true in both directions -or prove there isn't one.**- Joined
- 26 Nov '04
- Moves
- 148465

WhereverI'm not skilled enough at math to prove that there is no solution.

So I wrote a program and brute forced it. There is no solution.

Just for giggles, I allowed '0' to be one of the digits. The only solutions found all have at least one '0' in them. This is invalid for the problem, because a 2-digit number ending in 0 will not remain that way once reversed.

But it does give me some confidence that the program is correct.- Joined
- 18 Apr '10
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- 76676

S.Yorks.England@bigdogg

You are correct my friend.I'll type out the proof(answer) as given in the paper.*said*

I'm not skilled enough at math to prove that there is no solution.

So I wrote a program and brute forced it. There is no solution.

Just for giggles, I allowed '0' to be one of the digits. The only solutions found all have at least one '0' in them. This is invalid for the problem, because a 2-digit number ending in 0 will not remain that way once reversed.

But it does give me some confidence that the program is correct.

Hope you enjoyed the challenge.I wouldn't know where to start!

Reveal Hidden ContentThere isn't one.The equations can be written as 10a+b-10c-d=10e+f and 10f+e=10d+c-10b-a where the letters represent single digits.Subtracting the second equation from the first gives11(a+b-c-d)=9(e-f).This requires e-f to be divisible by 11which is impossible unless e=f then either a and b are both bigger than c and d or one of b or d is 0- Joined
- 18 Jan '07
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- 10608

30 Jun '22 18:36@venda

Ooh, I was so close and so far... I had it down to a multiple of 9 also being a multiple of 11, and never considered that, with these being digits, it would imply a number less than 10 being divisible by 11... Shame on me, really.*said*

You are correct my friend.I'll type out the proof(answer) as given in the paper.

Hope you enjoyed the challenge.I wouldn't know where to start!**Hidden content removed**- Joined
- 22 Apr '05
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- 613051

Linkenheim@venda

ha I had played around with a similar equation an d didn't see the*said*

You are correct my friend.I'll type out the proof(answer) as given in the paper.

Hope you enjoyed the challenge.I wouldn't know where to start!**Hidden content removed**

Reveal Hidden Contentdivisible by 11 part