What do you think?

bobbym · 2009-10-16 18:27:48

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)

bobbym · 2009-12-02 08:15:34

Hi;

This one is moderately hard.

Prob 3:

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

clandestine?

Anakin · 2009-12-03 19:31:34

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

bobbym · 2009-12-05 10:04:27

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.

Anakin · 2009-12-06 16:10:11

Wow, that mod stuff is confusing. <.<

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

bobbym · 2009-12-07 11:28:19

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.

mathsyperson · 2009-12-07 22:43:43

bobbym · 2009-12-08 04:39:10

Hi mathsyperson;

Correct!

bobbym · 2009-12-13 09:30:38

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!

phrontister · 2009-12-14 06:17:29

Hi Bobby,

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

Rasmushdahl · 2009-12-14 07:18:58

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

Rasmushdahl · 2009-12-14 07:45:36

I think I found out myself

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

bobbym · 2009-12-14 08:28:04

Hello Rasmus;

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

bobbym · 2009-12-14 09:35:20

Hello phrontister;

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

phrontister · 2009-12-14 22:54:39

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.

bobbym · 2009-12-15 06:17:28

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.

bobbym · 2009-12-23 11:50:28

Problem #7:

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

phrontister · 2009-12-23 12:02:20

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)

bobbym · 2009-12-23 12:05:24

Hi phrontister;

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

phrontister · 2009-12-23 12:12:48

Oops! <blush> Corrected it.

Found two more:

bobbym · 2009-12-23 12:28:05

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.

phrontister · 2009-12-23 12:35:50

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.

bobbym · 2009-12-23 12:37:55

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

phrontister · 2009-12-23 12:53:40

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)

phrontister · 2009-12-23 12:58:36

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)

Math Is Fun Forum

#1 2009-10-16 18:27:48

What do you think?

#2 2009-12-02 08:15:34

Re: What do you think?

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