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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

1) Can you find an integer b such that:

is a cube?

2)

This one can be a little tough.

10 people attend a raffle. The probability that 4 people at the raffle have the number n is .2508. What is the probability that a random person at the raffle has that number.

3) A guy owns a small casino. It only has one gaming table. He would like to earn 1000 dollars a day with it. There is only a flat bet of 2 dollars per roll and the players probability of winning is 18 / 37. The payoff is 2 dollars. How many games must be played on average for him to earn his 1000 dollars. Since he doesn't like to lose he needs to also know what is his chance of losing in any single day.

There were certain inconsistencies in the way this problem was phrased originally, this created problems in solving it. These were pointed out by All_Is_Number. I have modified it to have a clean solution.

*Last edited by bobbym (2009-12-02 08:12:01)*

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

This one is moderately hard.

Prob 3:

How many permutations of 3 letters can you make out of the word:

clandestine?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Anakin****Member**- Registered: 2009-10-04
- Posts: 145

I thought about the first one for a while and couldn't conjure up an answer. Mind posting the results in hidden text?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

Problem #4:

You can see 4 wire framed cubes stuck together and a spider at the upper left (A) and a fly at the bottom right,

How many paths can the hungry spider take to the immobilized fly? The spider is not a dummy. It always goes down and to the right (It can also take a diagonal). A to B, A to C and A to D are all legal. In short it always is crawling towards the fly. Also it must crawl along the wire edges of the 4 cubes.

Bonus: If there were 100 cubes stuck together instead of 4 and the fly was at the bottom right corner how many paths can the spider take?

Please hide your answers.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Anakin****Member**- Registered: 2009-10-04
- Posts: 145

Wow, that mod stuff is confusing. <.<

I'm gonna go Google it for a while and see if I come up with a result.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Here is a good one:

Problem #5:

You randomly choose 20 people. Find the probability that 5 of their birthdays are in the summer while 5 are in the winter. Of course all 4 seasons have the same number of months.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

Why did the vector cross the road?

It wanted to be normal.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi mathsyperson;

Correct!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Problem #6:

12 guys began to eat a cake. They ate it in the following order:

Bob ate 8.2% of the cake.

Moe ate 5.1% of the remaining cake.

Larry ate 3.8% of the remaining cake.

Curly ate 3.5% of the remaining cake.

Shemp ate 2.3% of the remaining cake.

Bud ate 9.1% of the remaining cake.

Lou ate 5.0% of the remaining cake.

Groucho ate 6.2% of the remaining cake.

Chico ate 11.3% of the remaining cake.

Harpo ate 1.66% of the remaining cake.

Zeppo ate 3.2% of the remaining cake.

Last, Milton ate 7.8% of the remaining cake.

At the end the remaining cake weighed exactly 352 grams. How many grams of the cake did Moe eat? Round to the nearest whole gram.

Don't forget to hide your answer!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

Hi Bobby,

*Last edited by phrontister (2009-12-14 06:30:26)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**Rasmushdahl****Member**- Registered: 2009-12-10
- Posts: 3

Hi Bobby and everyone

I'am new to this forum :-) My name is Rasmus and I come from Denmark. I would like to

post my answer, but i don't know how to hide it.

Rasmus

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**Rasmushdahl****Member**- Registered: 2009-12-10
- Posts: 3

I think I found out myself

*Last edited by Rasmushdahl (2009-12-14 07:46:45)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hello Rasmus;

Welcome to the forum! Also, congratulations that is correct! Well done!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hello phrontister;

I'm sorry I didn't see you up there. Very good! I knew you would get it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

Hi Bobby,

I only saw your solution to #1 just now, so I'll stop my little brute force Excel spreadsheet program. I was getting close to melting my cpu, anyway!

I'd just passed 2,600,000 (had starting with zero) for the test value of b (no solutions, of course), and still had quite a way to go before reaching b's maximum test value of 18,257,418 (after that, 3b²+3b+7 comes to more than Excel's 15 digit max.)

I was too lazy to try to work out a better brute force option, but it would have gone the same way...nowhere.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi phrontister;

Nothing wrong with that. Before I ever attempt to prove something I always let the computer try a couple of million examples, just to see if it might be true. Sometimes you find a counterexample for really small numbers.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Problem #7:

Find all the whole number x's that when multiplied by 434782608695652173913 yield all nines.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

bobbym wrote:

Find all the x's that when multiplied by 434782608695652173913 yield all nines.

Found one so far:

*Last edited by phrontister (2009-12-23 12:09:33)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi phrontister;

That's one! You can leave out the decimal point.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

Oops! <blush> Corrected it.

Found two more:

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Hi;

I am the one who should be blushing, I forgot to mention that x has to be a whole number. Am correcting the post. Sorry.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

Oh. I was just in the middle of typing out all the other decimal-place versions of that number when I saw your post.

Are there more answers than the one in my first post? I can't see how there could be.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Yes, there are an infinite amount of whole number answers. But they are very large.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

Are these the next two higher ones?

Yes...I can see that there are an infinite number of answers.

*Last edited by phrontister (2009-12-23 13:01:15)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,845

This is the largest answer my calculator can handle:

Used the copy/paste functions! And I didn't bother typing in the comma delimiters this time!

*Last edited by phrontister (2009-12-23 13:40:03)*

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