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I am working on a problem that involves the following:

One must find three numbers, integers and/or decimals, that multiply to ten.

Here's the catch:

You must use all integers, $0-9$, in the answer! So $1\times 2\times 5$ does not work.

I do not want the answer.

Instead, I ask if anyone has any ideas to which I can get as close to 10 as possible. The hint in the problem is that you cannot get to ten exactly, but close to it.

Right now, I have $1\times 2\times 5.0346789 = 10.0...$ Again, I do not want the answer, only a mathematical way to get to the answer. I cannot determine why I would be assigned this problem if it had no relation to mathematics.

Decimals ($\rm0.xxx$) count as use of the $0$, and you can place the zero at the end ($\rm x.xxx0$), too

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    @GerryMyerson: For instance, I don't think that it is easy, by hand, to arrive at solutions like $0.274 \times 5.983 \times 6.1 \approx 9.9999862$ or $0.26 \times 5.38 \times 7.149 \approx 10.0000212$ (neither of which is optimal BTW, because the OP doesn't want the answer).2011-10-16

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You could try programming a search that factors integers that are close to powers of $10$, and then examines the factors for their digits.

For example, $100002$ factors as $2\times3\times7\times2381$. Searching through possible triples of divisors, $6\times7\times 2381$ has unique digits (but is missing $4$, $5$, and $9$). If all digits were accounted for, this would lead to to $10.002=6\times7\times0.02381$.

(I'm not sure from your post if you are allowed to repeat digits, like how $0$ is repeated in this example.)

The search parameters would be which powers of $10$ you would examine, and also constraints on how far away from that power of $10$ you would roam. If digits aren't supposed to be repeated, I think $10^a$ with $a$ in $\left\{9,10,11\right\}$ would be appropriate. (And at this level, factoring shouldn't take the program too long.)

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    I found it! By rearranging the numbers in the example problem, I found the answer... too bad @ShreevatsaR put the answer on here EVEN THOUGH I ASKED EVERYONE NOT TO. Found it about ten days ago though; thanks for your help Ross and Alex2011-10-31
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So, you've started with $1\times2\times5$, and you've varied the 5 a little bit. Maybe you could try varying two of the three numbers, or all three of them.

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    1*2.053*4.8796 is what I have so far, and I think I am getting the hang of it, but do I still have to vary more to get what you are at?2011-10-16