Math riddle for you guys

[chuckywang]

I realized I made a mistake in the problem. This question showed up in my final this semester. I thought it was pretty neat.

Suppose you are trying to pick the results (win, lose, or tie) of 13 different football games one day. You can have as many submissions as you want. First prize goes to all the people who guess all 13 games correctly. Second prize goes to all the people who guess all but one game correctly. What is the least number of submissions you have to make in order for you to be guaranteed first or second place?

Note there are 3^13 number of different results.

 

[mugs]

Crap, 3 different outcomes for each game and it's still less than 4096?

 

[Goosemaster]

Originally posted by: mugs
Crap, 3 different outcomes for each game and it's still less than 4096?

:laugh:

 

[Random Variable]

I'm now getting 59,049

 

[Goosemaster]

whoops...didn't finish the math..one sec

 

[Goosemaster]

Originally posted by: Random Variable
I'm now getting 59,049

LOFL

 

[HermDogg]

Who's got the bye?

 

[Goosemaster]

96?

 

[conehead433]

Well you changed the parameters of the problem by including the possibility of a tie. Therefore there are 3 possibilities for each of 13 games. 39 X 13 = 507 minus 1 incorrect game would be 506.

Edit: With only having to get 12 games correct it should only be 39 x 12 = 468. My bad.

 

[Random Variable]

The probability of getting at least 12 games right is 1/59049, so wouldn't that mean that the number of submissions would need to be at least 59,049?

Adding the "tie" option makes it confusing. I give up.

 

[Goosemaster]

Originally posted by: conehead433
Well you changed the parameters of the problem by including the possibility of a tie. Therefore there are 3 possibilities for each of 13 games. 39 X 13 = 507 minus 1 incorrect game would be 506.

whoops.....I got the same thing


<-----stil out of it from xmas

 

[chuckywang]

Originally posted by: Random Variable
The probability of getting at least 12 games right is 1/59049, so wouldn't that mean that the number of submissions would need to be at least 59,049?

Yes, keep thinking along that track.

 

[Ready]

the answer is 5

 

[chuckywang]

Originally posted by: Goosemaster

Originally posted by: mugs
Crap, 3 different outcomes for each game and it's still less than 4096?

:laugh:

No, it's not less than 4096 anymore.

 

[mugs]

n/m

 

[conehead433]

Originally posted by: conehead433
Well you changed the parameters of the problem by including the possibility of a tie. Therefore there are 3 possibilities for each of 13 games. 39 X 13 = 507 minus 1 incorrect game would be 506.

Edit: With only having to get 12 games correct it should only be 39 x 12 = 468. My bad.

Hopefully this is correct.

 

[Goosemaster]

531441

 

[MBrown]

13

 

[chuckywang]

Originally posted by: Goosemaster
531441

way less than that.

 

[Goosemaster]

Originally posted by: chuckywang

Originally posted by: Goosemaster
531441

way less than that.

has anyone gotten it yet?

 

[chuckywang]

Originally posted by: conehead433

Originally posted by: conehead433
Well you changed the parameters of the problem by including the possibility of a tie. Therefore there are 3 possibilities for each of 13 games. 39 X 13 = 507 minus 1 incorrect game would be 506.

Edit: With only having to get 12 games correct it should only be 39 x 12 = 468. My bad.

Hopefully this is correct.

I can't follow your reasoning and your answer isn't correct.

 

[chuckywang]

Originally posted by: Goosemaster

Originally posted by: chuckywang

Originally posted by: Goosemaster
531441

way less than that.

has anyone gotten it yet?

Someone posted the correct answer but hasn't explained.

 

[KingofCamelot]

36?

I say 36, because if you put win down for both teams in all but one game (12 x 2), and then put tie for all 12 of those games as well, you've covered all your bases to secure second place with only 36 submissions. Atleast that was my logic, its probably flawed though.

 

[mugs]

Originally posted by: chuckywang

Originally posted by: Goosemaster

Originally posted by: chuckywang

Originally posted by: Goosemaster
531441

way less than that.

has anyone gotten it yet?

Someone posted the correct answer but hasn't explained.

So it's either 13, 5 or 96? Those are the only ones I see with no explanation that you haven't shot down yet.


Edit: Unless it's 59049 and you just mean they haven't explained it thoroughly enough...

 

[PhilsPhan]

Correct answer is 531441. There are 3 possible outcomes to each game. Therefore you have a 1/3 chance of guessing correctly for each game. Only need 12 games right. Thus it is 1/3^12 *1 (3/3 the last game it doesn't matter if it is right or wrong.)