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Problem of the Week; |*---The Problem of the Week---*| 12/15
Topic Started: Dec 16 2006, 02:56 AM (801 Views)
Michel
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Chipmunk
Smarty Pants
Wait...is it sad that you agree with me, or sad that no one solved the problem?
You cannot shake hands with a clenched fist.

-Indira Gandhi (1917 - 1984)
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Myself
Smarter than the Average Amoeba
[ * ]
Admin
Dec 15 2006, 05:56 PM
Persistent Numbers
-------12/15/06-------


A persistent number is a number that, if multiplied by any positive integer the resulting number always contains the ten digits 0, 1, 2,...,9 in some order with possible repetitions.

Prove that there are no persistent numbers.

:scratchhead:

OK, since no one is getting this, I will guess. And guess wrong I will. This is in no means a real 'proof.'

Any number multiplied by two (or any even number) will have all of its digits double, therefore no odd numbers will remain in the product (except several ones.)

Hey - don't make fun of me. At least I TRIED. :ppbbhtt:

P.S. - NEW QUESTION!!
muahahahahahahahaha sorry. modhax.
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Michel
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37 * 2 = 74.

7 is odd.

Good try though.
You cannot shake hands with a clenched fist.

-Indira Gandhi (1917 - 1984)
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Myself
Smarter than the Average Amoeba
[ * ]
This is the problem of the WEEK, not the problem of the month. No one is solving it, can't we get a new question?
muahahahahahahahaha sorry. modhax.
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Michel
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Admin doesn't appear to like doing that...I'll pester him tomorrow.
You cannot shake hands with a clenched fist.

-Indira Gandhi (1917 - 1984)
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Admin
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Admin
Solve the problem and it will be changed.


Good try Myself, but it's a bit more complicated than that.
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Michel
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What if I prove that there are some?
You cannot shake hands with a clenched fist.

-Indira Gandhi (1917 - 1984)
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Admin
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Admin
Then do so and I will consider it solved. Good luck, though, on that....
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Myself
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Okay, I think I have it.

X = persistent #
(n)(X) = persistent number
(n) = number

Let's say we make n = 3.

3X = persistent #

Now let's divide by 3.

X = (persistent number)/3

Since X is a persistent number, that would mean...

persistent # = (persistent #)/3

Therefore, no persistent number can be multiplied by 3.
muahahahahahahahaha sorry. modhax.
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Admin
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You missed the fact that the persistent numbers will be different. Obviously through the way you defined it, persistent #1 = (persistent #2)/3.
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