A number double the size when reversed.

A number double the size when reversed. - Printable Version

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A number double the size when reversed. - Mrkrabz - 28.08.2012

I don't know if this is possible or not, also don't ask why I need this

So basically you have a number lets say 456, when written backwards 654 it needs to equal exactly double the first number (456) Is there a number out there that does this? I cant find one. That's if it's even possible.

No pun intended with my username.

Re: A number double the size when reversed. - Mauzen - 28.08.2012

Interesting question..
Think like a computer!
This script I just wrote can find such numbers (if exisiting).
Note that its just functional to do what you need, no eye given to speed

pawn Код:

stock findRev(min, max)
{
    for (new i = min; i <= max; i++) {
        if (reverseNumber(i) == 2 * i) printf("%d is a reverse-magic number!", i);
    }
}

stock reverseNumber(num)
{
    new t[12], n[12];
    format(t, 12, "%d", num);
    new slen = strlen(t);
    for (new i = 0; i < slen; i++) {
        n[slen - i - 1] = t[i];
    }
    return strval(n);
}

This does not return any result except 0 for the first million numbers.
Explanation why such a number cant exist is following as soon as I made up my mind

Re: A number double the size when reversed. - Finn - 28.08.2012

It's impossible...

Re: A number double the size when reversed. - Extremo - 28.08.2012

The number can't exist for one simple reason:

No matter what order you place the numbers, one number will always result in not being the exact double of the one before simply because when they switch places, their value never changes.

Look at this example:

428

Now reversed, the first digit matches, it becomes an 8 which is a double of a 4. The second digit becomes a 2, which is equal to the digit before. The last part becomes a 4 which is half of the digit before. Let's not focus on the reasons for the outer digits but primarily the middle one. There is already one problem. On every unevent digit count, one digit never moves and thus can never be exchanged by a digit that could be times two the size.

Another problem is this:

48

Reversed, the first digit would equal 8, which is double of 4 but there is a big catch to this. Because you previously know that if your first digit is four, your second digit must be 8. However in reverse, 8 will be replaced by 4 which is half of the original digit.

There are a sum more problems that can occure and for these simple reasons, I do not believe there can be a number that reversed is equal the size times two.

Re: A number double the size when reversed. - mamorunl - 28.08.2012

Oh god,, I just thought by myself "Well, that is an explanation that Extremo would give" then I looked at your name.. and I went "OMG"... so ya..

Nice explanation though (and dont chat me up at 5 in the morning. I woke up because of that... skype is on, on my phone ><)

Re: A number double the size when reversed. - Si|ent - 28.08.2012

The only answer is Zero, 0

Re: A number double the size when reversed. - Mrkrabz - 28.08.2012

Quote:

Originally Posted by Si|ent

The only answer is Zero, 0

I ran all the way up to 10million, guess you are right.

Re: A number double the size when reversed. - Extremo - 29.08.2012

Quote:

Originally Posted by mamorunl

Oh god,, I just thought by myself "Well, that is an explanation that Extremo would give" then I looked at your name.. and I went "OMG"... so ya..

Nice explanation though (and dont chat me up at 5 in the morning. I woke up because of that... skype is on, on my phone ><)

Well.. thank you!

(I tried at 5am and you werent there! Then the next day I tried at 6am. When the heck do you wake up?)

EDIT:

I just saw Zero being mentioned, but Zero is not double of itself. If Zero was double of itself, it'd also be tripple of itself and so forth until infinity. That doesn't make any sense.

Here's another easy explaination that may help:

Any number:

234823478923894923847892378942384

Cannot be double of itself reversed, here's why:

234823478923894923847892378942384

Now, the numbers at each end will always replace each other. So, 2 becomes 4 and 4 becomes 2 and that's already the catch to it.

2 becomes 4 (doubled).
4 becomes 2 (halfed).

No way this could ever be possible.

Re: A number double the size when reversed. - Si|ent - 29.08.2012

Zero is unique. It IS double itself, (2 x 0 = 0) and triple, etc. To infinity.
This is why it is the ONLY number that works for this self-imposed problem.

Re: A number double the size when reversed. - Extremo - 29.08.2012

Quote:

Originally Posted by Si|ent

Zero is unique. It IS double itself, (2 x 0 = 0) and triple, etc. To infinity.
This is why it is the ONLY number that works for this self-imposed problem.

I disagree.

Now, let's elaborate what I believe is double in size.

4 is double the size of 2, now how do I know that? Well, our ancestors invented math to calculate realistic things. When speaking of realistic things, language describes realistic things. Now, let's see a caveman here who has brought back two eggs. He knows that with his wife together, both may only eat 1 egg. 2/2 = 1

Let's extend that concept to the zero.

The caveman found 0 eggs. Now he wants to know how much he can share with his wife and it turns out he cannot share anything a.k.a. nothing.

Now, if you look at this concept, what is double the size of nothing? Something. We could go ahead and say 1 is double the size of 0 but that wouldn't be entirely true either.

There is actually nothing that is double of nothing. You cannot double nothing in anyway. So, assuming the literal question, nothing remains nothing and thus is still nothing. Size however evaluates value. Zero is a value. Zero multiplied by Two is still Zero. The value has thus not changed and it is not double of itself. There is no double the size value for zero, at least none that couldn't be broken into decimals.

So thus, the correct answer in my opinion would be that there is no mathematical correct number which reversed has double it's value. It simply doesn't exist.

You cannot tell me that a mathematical operator such as a multiplication defines the size of the value that the multiplication returns. The return defines the value, not the multiplication itself!

Otherwise I could well have explained how the universe came to existence out of nothing! I guess God or whom ever you believe or what ever you believe may have created the universe must of just multiplied the Zero with TWO! HOLY COW!

(PS: I hope you don't mind sarcasm/irony)
Regards.