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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

Hi;

1 x 2 x 3 x 4 x 5 x 6 x ... x 55

Is less than

100 x 100 x 100 x 100 x 100 x100 x ... x 100

So 55! is less than 10^110. This is a rough upper bound.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

Hi;

Is that the answer for K, then what is P?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

Hi;

Yes, that 103 is correct. You can do it by the number of trailing zeroes of a factorial.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

Hi;

I have a formula that is close but not yet exact, I will work on it and post when I get it.

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**If it ain't broke, fix it until it is.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

Hi;

One question at a time. The answer I believe for the factorial problem.

1) Compute the highest power of 2 in 10000! which is 9995.

2) Compute the highest power of 2 in 100! which is 97

3) Divide 9995 by 97 and take the floor value. You get 103.

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**If it ain't broke, fix it until it is.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

The highest power gives 104 which is one too many. The smallest power seems to give the right answer. I am not sure why but it is working.

For instance:

It gets k = 1030 which is correct.

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**If it ain't broke, fix it until it is.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

1030 is correct for 100000!. 103 is correct for 10000!.

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**If it ain't broke, fix it until it is.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

No problem. Please post your remaining questions in Help me. Start a new thread there, this thread belongs to Ganesh's questions.

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**If it ain't broke, fix it until it is.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

Hi;

You can not post a link until you have been here a while. Open up a new thread and I will fill in the link.

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**If it ain't broke, fix it until it is.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,201

That is what you use, post new topic. Press that and you be able to post your question.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

**Online**

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