### Brain Teasers

# Twice Shy

Steven was writing out an equation in English, when he realised that if he multiplied ten by two, his answer (twenty) also had twice as many letters as the word ten.

Ten (3 letters) x2= Twenty (6 letters)

How many other integers are there that if you double the number, you get an answer with twice the number of letters?

Ten (3 letters) x2= Twenty (6 letters)

How many other integers are there that if you double the number, you get an answer with twice the number of letters?

### Answer

4.Six (3 letters) x2= Twelve (6 letters)

Nine (4 letters) x2= Eighteen (8 letters)

Fifty (5 letters) x2= One Hundred (10 letters)

Fifty One (8 letters) x2= One Hundred and Two (16 letters)

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## Comments

If, like me, you don't consider AND to be part of the written form of an integer, then 51 doesn't work, but 56 and 59 do work.

AAAArrrrggghhh!!!! Not the "And" in a number problem again

Sorry >.<

If you are saying (for example) "one hundred and eleven" it has an "and" in it, so I think it's fair to say that if you are writing it down in English it will have those three letter in it.

Any way, I hope you liked the teaser.

If you are saying (for example) "one hundred and eleven" it has an "and" in it, so I think it's fair to say that if you are writing it down in English it will have those three letter in it.

Any way, I hope you liked the teaser.

Can you prove that there are not others?

By my reasoning anything over a hundred is not going to work... though I'm not sure if you start using number bigger than those I know (like quinvigitillion or something)

The most that any number can double to is one decimal place higher than itself and thus doubling tends to end up with close to the same number of letters or lless than with higher numbers like "one hundred and four million" and "five hundred thousand".

I don't know if any negative numbers work but seeing as twisting things so that you end up with "minus six" Ã—2 = "negative twelve" still leaves you falling short I'd say that negatives don't work either.

If you can find any others I will be in awe of you.

The most that any number can double to is one decimal place higher than itself and thus doubling tends to end up with close to the same number of letters or lless than with higher numbers like "one hundred and four million" and "five hundred thousand".

I don't know if any negative numbers work but seeing as twisting things so that you end up with "minus six" Ã—2 = "negative twelve" still leaves you falling short I'd say that negatives don't work either.

If you can find any others I will be in awe of you.

clarification on the "and" business - "and" is NOT part of the word, it is a misconception that it is allowable to say "and". "one hundred and eleven" really means 100.11, as "and" can represent a decimal, but not merely a break in the middle of the number.

lessthanjake,

thanks very much for your input.

I think, however, that the conventions differ according to which country you were schooled in.

thanks very much for your input.

I think, however, that the conventions differ according to which country you were schooled in.

I think Atty's right. I still don't like her though... too hard

"and" is included on British English; it is NOT included in American English.

So in American English:

sixty seven * 2 = one hundred thirty four

eighty four * 2 = one hundred sixty eight

I know the puzzle specifies integers, but fractions do use "and", so:

two thirds * 2 = one and four twelfths

Then there are decimal equivalents:

one tenth * 2 = zero point two zero

Then there is scientific notation:

sixty four thousand * 2 = one point two eight times ten to the fifth

I'm guessing there are some other solutions out there.

So in American English:

sixty seven * 2 = one hundred thirty four

eighty four * 2 = one hundred sixty eight

I know the puzzle specifies integers, but fractions do use "and", so:

two thirds * 2 = one and four twelfths

Then there are decimal equivalents:

one tenth * 2 = zero point two zero

Then there is scientific notation:

sixty four thousand * 2 = one point two eight times ten to the fifth

I'm guessing there are some other solutions out there.

I think that this was already explained in earlier comments, so I'm not sure that it's very relevant.

Thanks all the same though.

Thanks all the same though.

Not sure which of my points you mean were discussed previously--I'm guessing it's the "and" stuff. Nobody pointed out *why* there is so much disagreement on the issue: it's a British English vs. American English issue.

Anyway, I did give some additional integer solutions. I'm kind of particular to

sixty four thousand * 2 = one point two eight times ten to the fifth (34 letters)

Anyway, I did give some additional integer solutions. I'm kind of particular to

sixty four thousand * 2 = one point two eight times ten to the fifth (34 letters)

There were several problems early on in the Braingle database that had this same UK/USA English issue so I thought that I had been clear enough in my explanation. Thanks for the further clarification.

Your answer:

sixty four thousand (seventeen letters)

one point two eight times ten to the fifth (thirty four letters)

--

Yes, that's very impressive.

How long did it take you to figure that one out?

Your answer:

sixty four thousand (seventeen letters)

one point two eight times ten to the fifth (thirty four letters)

--

Yes, that's very impressive.

How long did it take you to figure that one out?

I don't recall how long each one took. I probably spent fifteen or twenty minutes on all the answers together. I always try to find multiple answers for teasers like this before looking at the answer so that at least one of mine will be different.

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