Reversing a Number
You can get a reverse of number only by multiplying the number by X or Y ? Find X, Y ?
Assume the number is not a palindrome.
if you are wondering, reverse of ABC = CBA
Assume the number is not a palindrome.
if you are wondering, reverse of ABC = CBA
Labels: mathemagic
posted by ToM at
9:23 AM
38 Comments:
This post has been removed by the author.
The question doesn't make sense.
Assuming ABC is the number, then ABC*X=CBA and ABC*Y=CBA then either X=Y or ABC=0 or both. As 0 is a palindrome ABC<>0 so X=Y. But the question implies that X<>Y.
Would you please write the question more clearly.
This post has been removed by the author.
if you allow X or Y to be any number including non whole numbers, then the answer would be an infinite amount.
e.g. 123 X 2.6097 = 321
Tom, did you mean that it is possible to reverse some number(s) by multiplying them by X, and that there are some other number(s) that can be reversed by multiplying them by Y?
This could be a good problem about to be wasted because it was poorly expressed.
Hi Anonymous. Your answer is in an approximation. Even if you had answered exactly, you would simply write X=CBA/ABC and have a general solution. That's a trivial interpretation of the problem. If that same X also reverses other numbers, that's another story. But is only interesting if you can determine what those other numbers are.
I'm not knocking you, I find the question very difficult to interpret.
Also bear in mind that ABC is just an illustration, the "number" may, a priori, have any number of digits.
I can't believe the problem isn't intended to be a genuine challenge.
This post has been removed by the author.
There is nothing to suggest that the problem is or isn't confined to integer, rational or real values.
It is often the unwritten law that that such problem are meant to be solved with integers only.
002 x 100 = 200 .....lalalala....
LOL
This post has been removed by the author.
i think what tom means is this : there is a 2digit number, XY and if THIS number is multilied by x or y it will be reversed.....
but i still cant find any number like that
and the ABC thing is just an example i dont think it is needed if u noe what reverse is.
This post has been removed by the author.
A. Without employing the ancient and venerable practice of triple lobotomy, I cannot reconcile your interpretation with the posed problem by any stretch of my imagination.
You're right about the ABC thing. I never thought otherwise.
The ONLY number X that reverses ABC has to be CBA/ABC. X would be unique for most values of ABC, except for simple multiples, e.g. 321/123 = 642/246 = 107/41.
And there can be no value of Y that is different from X.
Same reasoning applies to any number of digits: ABCDE...
So, what's the challenge?
Hi Anonymous. I absolutely agree with you.
I'm so irritated that the problem hs been ruined by bad phraseology and grammar and that Tom hasn't deigned to notice that there is a problem with his problem. It's not even grammatical "...reverse of number..."
TOM, PLEASE DELETE THIS BLOG AND POST IT AFRESH WITH CLEARER INFORMATION.
Thank you.
The problem is quite simple , i think you guys are trying to read between the lines.
let's say IF
124 * x = 421
x is a 1 digit integer you have to find that
This phenomenon only occurs for a some unique values.
now 101 is a palindrome
and 101 * 1 = 101, so 1 cannot be an answer here
This post has been removed by the author.
This post has been removed by the author.
This post has been removed by the author.
Tom, now I know that X and Y are single digits numbers (not stated in the question and definitely have to read between the lines to get that info) I see that it is a non-trivial problem as I had assumed. Thanks for the info.
This post has been removed by the author.
This post has been removed by the author.
OK, by programming know what to aim for.
X = 4 => N = 2178, 21978, 219978, 2199978 etc.
Y = 9 => N = 1089, 10989, 109989, 1099989 etc.
But that's cheating and also doesn't guarantee that the sequence is as simple as it seems.
I also realise that X,Y being 1 digit is a logical necessity.
I nearly interpreted the question correctly at one stage, but thought that's not what the question says it's asking for.
This post has been removed by the author.
...and I was right.
The next 2 in the 4 sequence are 21782178 and 21999978
The next 2 in the 9 sequence are10891089 and 10999989
And there is no way to be sure that another and another sub-variation doesn't occur.
Also not proven that 4 and 9 are the only possible X,Y values.
This post has been removed by the author.
This post has been removed by the author.
Using ABC*X=CBA I made a (1 digit)table of A as the product of C*X. A = 0 isn't allowed so got rid of a few cells, then I used A*X < C+4 or 10 to eliminate loads more, leaving:
X = 4, A = 2, C = 8
Y = 9, A = 1, C = 9
are the only possibilities. More deductions later perhap!
Examing the next level in =>
X = 4 => 21..78
Y = 9 => 10..89
Can say a little more about the second digit in.
This is starting to become tedious, and the explanatory content is becoming harder to include, so I'm stopping here.
Just for the record, I didn't and haven't checked specifically the case for a 2 digit number such that AB*X=BA.
Chris, in the problem, when it said reverse of ABC=CBA, it was not saying anything about X or Y, it was using that as an example. the answer would be something like 2X=X2, which cannot be done, so the answer to the whole thing is "no, you cannot get a reverse of number only by multiplying the number by X or Y, even if it is not a palindrome" now if it were
2X=3Y, then yes that could be done, for the answer would simply be 3Y=2X.
This post has been removed by the author.
This post has been removed by the author.
This post has been removed by the author.
This post has been removed by the author.
This post has been removed by the author.
Jacob. I've already given 12 results that you say are impossible.
An example is: 4 * 2178 = 8712
I can't work out your interpretation of the problem.
Post a Comment
Links to this post:
Create a Link
<< Home