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**ravengirl****Member**- Registered: 2006-09-22
- Posts: 4

My daughter came up with a good one last night and it kept me awake hugging my calculator for hours before I could finally give up and go to sleep. Here is the question... how many times would you have to multiply 28 to get an answer where all of the numbers in the answer are the same... got me... can someone help? Its driving me crazy and I just dont want to look stupid lol we all like to impress our kids

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I believe the answer is that there exists no answer. Anyone want to conjure up a proof?

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Are we talking about multiplying 28 by other numbers or multiplying it by itself? 28n or 28^n?

I have a feeling Ricky's right either way though. But I have no idea how it could be proved.

Why did the vector cross the road?

It wanted to be normal.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I interpreted it 28^n.

The proof wouldn't be too hard. First prove that 28^n is even. That is, it ends in a 0, 2, 4, 6, or 8. Then prove there must be at least one odd number in it. That will be a bit more tricky.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**ravengirl****Member**- Registered: 2006-09-22
- Posts: 4

multiplying by other numbers.. apparently she says there IS an answer.. i cant find it lol

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

oh thats easy, its 0

0*28 = 0, and every digit of the number 0 is the same

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**ravengirl****Member**- Registered: 2006-09-22
- Posts: 4

omg it must be nice to be a genius LOL thanks so much.. god i really feel stupid now lol

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Well, ricky said there are none, luca said the number 0 - I say there are an infinite amount of solutions. The question was "how many times". We weren't told that it had to be natural numbers, so do I need to say more than Q?

where y can only be made of identical digits.this one satifies it, doesnt it?

and this?

of course it's just about keeping the upper part(so sorry, don't the english term.. "tæller" in danish ) made of the same numbers. 111,33333,444444,5555555.... They should all work

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**ravengirl****Member**- Registered: 2006-09-22
- Posts: 4

This is the question she posed to me.. I guess I should have just typed it out in the first place sorry not trying to confuse anyone here...

Lisa, went shopping for tiles at the local shop the other day. The tiles were on sale for only 28 dollars each.

However, she got it in her head that, for good luck, the total amount of dollars she must spend must be a number where all of the digits are the same.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Well, then it's a whole other story Then my best answer is 0 aswell

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**espeon****Real Member**- Registered: 2006-02-05
- Posts: 2,586

what answer did ur daughter give? i hope i dont get a problem like this at school.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Let's see if we can find an answer other than 0. Well, first off, we know that 28 = 4*7, so whatever number we find must have both of those as factors.

To determine whether a number is divisible by 4, you look at its last 2 digits. The only 2-digit numbers that have all their numbers the same and are divisible by 4 are 44 and 88.

So whatever number you pick will be made up of a load of 4's or a load of 8's and will have to be divisible by 7. And in fact, since 444... is a factor of 888..., we can get away with only trying chains of 8's.

Let's try some then.

8/7 = 1.14... NO

88/7 = 12.57... NO

888/7 = 126.86... NO

8888/7 = 1269.71... NO

88888/7 = 12698.29... NO

888888/7 = 126984. Success!

And as the quotient is even, we can tell that 444444 will also work.

So the answer is 444444/28 = 15873 times.

Either your daughter is very intelligent or she pressed the equals button on her calculator a lot of times.

Why did the vector cross the road?

It wanted to be normal.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

or the teacher asked the question in school

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