Exactly Doubled

[kuiperbelt]

A genuine mathematical question:


Find a number so that when its last digit is put in front, the number is exactly doubled.




eg 1. 25 becomes 52 (slightly more than doubled)

eg 2. 112 becomes 211 (which is a bit less than doubled)

[ToraToraTora]

You mean first digit?

[bobbinwales]

No... see the two examples Ttt

[ToraToraTora]

you mean first digit put in front?

[bobbinwales]

No.. move last digit ( units) to the front

[Old_Geezer]

Yes.

Suspect it will be at least 3 digits long as a quick think about how 2 digit numbers fare suggests they don't work.

So, not really a trial & error type thing.

[Old_Geezer]

Look at eg2

The last digit '2' was moved from the units to the hundreds column, the rest shuffle down.

[ZebuSanctuary]

Try this number;

105,263,157,894,736,842

Put into words; one hundred and five quadrillion, two hundred and sixty three trillion, one hundred and fifty seven billion, eight hundred and ninety four million, seven hundred and thirty six thousand, eight hundred and forty two.

Now take the last digit '2' and place it in front of the number;

210,526,315,789,473,684

which is exactly double 105,263,157,894,736,842

:-)

[ToraToraTora]

sorry quite right!

[ToraToraTora]

That's a big number, I wrote a program to find a smaller one found nothing up to 5m.

[ToraToraTora]

I also tried it with the first number put at the end, same result.

[ClareTG0ld]

What's all the more impressive is that Zebu actually check every number up that by hand. Remarkable.

[elliemay1]

Hope the next 1% question isn't like that!