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**Mathegocart****Member**- Registered: 2012-04-29
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1.How many unique sets of 4 prime numbers exist for which the sum of the members of the set is 45 ?

2. Bobbym wrote on a gigantic piece of paper all the numbers from 1 to 9999 . How many zero digits did he have to write down?

3. Find

.

4. Find x.

5. Which is greater?

[edited by admin](he latexed my post, gratitude to BOBBYM.

6. Find the sum of all perfect squares that divide 2016.

7. Find the greatest possible value of pq + r, where p, q, and r are (not necessarily distinct) prime numbers

satisfying pq + qr + rp = 2016.

8. Positive integers m and n are both greater than 50, have a least common multiple equal to 480, and have a

greatest common divisor equal to 12. Find m + n.

9. Bobbym is stuck fighting his nefarious lizard neighbors yet again though he has another weapon in his math... A LASER! He has 15 health, and the lizard has 20 health. He can deal any integer amount of damage from 1 to 4 and he has a 1/5 chance of dealing 3 damage, a 1/2 chance of dealing 1 damage, and a 1/5 chance of dealing 2 damage, and a 1/10 chance of deleaing 4 damage. Calculate the probability that bobbym will make it out alive, given that bobbym strikes first. The lizards have a 50% chance of dealing 1 damage, and a 50% chance of dealing 2 damage.

10. Find all continuous functions such that

and

*Last edited by Mathegocart (2016-08-30 04:45:39)*

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I think you're missing some information in #5.

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**bobbym****Administrator**- From: Bumpkinland
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Hi;

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**Mathegocart****Member**- Registered: 2012-04-29
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Fixed.(5)

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**bobbym****Administrator**- From: Bumpkinland
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Are you sure?

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**Mathegocart****Member**- Registered: 2012-04-29
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bobbym wrote:

Hi;

Everything is correct, and I have fixed problem number 5.(VERIFIED.)

*Last edited by Mathegocart (2016-08-28 11:18:46)*

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**bobbym****Administrator**- From: Bumpkinland
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Number 5 is rather easy, are you sure that is what you want? I need more for 9.

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**Mathegocart****Member**- Registered: 2012-04-29
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I meant .

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**bobbym****Administrator**- From: Bumpkinland
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Number 9 requires more information. What happens at the endpoints and what kind of damage does the large lizard do?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Mathegocart****Member**- Registered: 2012-04-29
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bobbym wrote:

Number 9 requires more information. What happens at the endpoints and what kind of damage does the large lizard do?

Didn

't I already specify what kind of damage he does? And how much damage you deal?

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**bobbym****Administrator**- From: Bumpkinland
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Sorry, yes you did.

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**Mathegocart****Member**- Registered: 2012-04-29
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bobbym wrote:

Sorry, yes you did.

I just wanted to verify.

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**thickhead****Member**- Registered: 2016-04-16
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*Last edited by thickhead (2016-08-28 19:54:32)*

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**bobbym****Administrator**- From: Bumpkinland
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Hi Mathegocart;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**thickhead****Member**- Registered: 2016-04-16
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**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**Mathegocart****Member**- Registered: 2012-04-29
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bobbym wrote:

Hi Mathegocart;

The battle is, indeed, described in this manner.

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**Mathegocart****Member**- Registered: 2012-04-29
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thickhead wrote:

Wait, what? One of his acquaintances is named Liz?

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**bobbym****Administrator**- From: Bumpkinland
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Not that I know of.

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**thickhead****Member**- Registered: 2016-04-16
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(2)

No.of 0's in unit place=9999 div 10=999

No. of 0's in tens place=10*(9999 div 100)=990

No. of 0s in hundred place=100*(9999 div 1000)=900 Total=2889

No of any other digit=( 9999 div 10+1)+10*(9999 div 100+1)+100*(9999 div 1000+1)+1000*(9999 div 10000+1)=4000

**{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha{Gods rejoice at those places where ladies are respected.}**

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**Mathegocart****Member**- Registered: 2012-04-29
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thickhead wrote:

(2)

No.of 0's in unit place=9999 div 10=999

No. of 0's in tens place=10*(9999 div 100)=990

No. of 0s in hundred place=100*(9999 div 1000)=900 Total=2889

No of any other digit=( 9999 div 10+1)+10*(9999 div 100+1)+100*(9999 div 1000+1)+1000*(9999 div 10000+1)=4000

Strange, because with casework, I have gotten the same solution as bobbym has. I will check if I made a naive mistake, but..

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**thickhead****Member**- Registered: 2016-04-16
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My solution is same as bobbym's. Only i have added result for any digit other than 0.

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