Need a math geek to solve a problem

[erikvonb]

A guy at work wants to figure this one out...

There are 14 different football games being played. He wants to bet on all 14 games. Wins only.

How many different tickets would he have to play to cover every possible scenario?

If you could post the formula too, that would be appreciated.


-Erik

 

[jersey_emt]

Each ticket has all 14 games on it?

 

[jersey_emt]

If so, there are 2^14 possible scenarios (16384)

 

[erikvonb]

Each ticket has all 14 games on it?

yes. 14 games on each ticket.

 

[erikvonb]

If so, there are 2^14 possible scenarios (16384)

so...you're saying 2 raised the the 14th power? (2 possible outcomes for each game, and 14 different games)

I thought the number would have been higher.


-Erik

 

[peepsalot]

28 tickets would cover every scenario. Is that supposed to be a trick question? Or does one ticket cover 14 games simultaneously. I've never bet on games.

 

[Spooled]

jersey got it.

 

[Spooled]

00000000000000
10000000000000
01000000000000
00100000000000
00010000000000
00001000000000
00000100000000
00000010000000
00000001000000
00000000100000
00000000010000
00000000001000
00000000000100
00000000000010
00000000000001
11000000000000
10100000000000
10010000000000
10001000000000

and so on and so on. That's a lot of tickets by the way.

 

[erikvonb]

28 tickets would cover every scenario. Is that supposed to be a trick question? Or does one ticket cover 14 games simultaneously. I've never bet on games.

28 tickets would definitely not cover it. There are 28 different teams playing (14 games) and you are betting on the outcome of every game...with all 14 games on each ticket.

-Erik

 

[BradC]

00000000000000
10000000000000
01000000000000
00100000000000
00010000000000
00001000000000
00000100000000
00000010000000
00000001000000
00000000100000
00000000010000
00000000001000
00000000000100
00000000000010
00000000000001
11000000000000
10100000000000
10010000000000
10001000000000

and so on and so on. That's a lot of tickets by the way.

And no way to bet efficiently enough to make money!

 

[65racecoupe]

28 tickets would cover every scenario. Is that supposed to be a trick question? Or does one ticket cover 14 games simultaneously. I've never bet on games.

What this means is....

To cover every senario and gurantee 1 winning ticket, you have to buy many. It is like a combo lock. 1,2,3,4,5, nope. Ok, 1,2,3,4,4, nope, Ok, 1,2,3,4,3......and so on.

Instead of numbers on the lock, you have teams, 28 of them. 14 have to win, all on one ticket.

I would think that the number is higher. Don't you have to use 28 teams instead of 14 wins as your numbers for the formula?

 

[hazeXban]

14 games, 2 outcomes possible. and actually if a game ties thats a push making the whole ticket a loss. so tecnically it should be

3^14
which is
<TABLE style="WIDTH: 48pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=64 border=0 x:str><COLGROUP><COL style="WIDTH: 48pt" width=64><TBODY><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 48pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" align=right width=64 height=17 x:fmla="=3^14" x:num>4,782,969</TD></TR></TBODY></TABLE> tickets

 

[erikvonb]

What this means is....

To cover every senario and gurantee 1 winning ticket, you have to buy many. It is like a combo lock. 1,2,3,4,5, nope. Ok, 1,2,3,4,4, nope, Ok, 1,2,3,4,3......and so on.

Instead of numbers on the lock, you have teams, 28 of them. 14 have to win, all on one ticket.

I would think that the number is higher. Don't you have to use 28 teams instead of 14 wins as your numbers for the formula?

I would have thought it was higher, but either way, you wouldn't be making any money.

 

[erikvonb]

14 games, 2 outcomes possible. and actually if a game ties thats a push making the whole ticket a loss. so tecnically it should be

3^14
which is
<TABLE style="WIDTH: 48pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=64 border=0 x:str><COLGROUP><COL style="WIDTH: 48pt" width=64><TBODY><TR style="HEIGHT: 12.75pt" height=17><TD style="BORDER-RIGHT: #d4d0c8; BORDER-TOP: #d4d0c8; BORDER-LEFT: #d4d0c8; WIDTH: 48pt; BORDER-BOTTOM: #d4d0c8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" align=right width=64 height=17 x:num x:fmla="=3^14">4,782,969</TD></TR></TBODY></TABLE>tickets

Well, in our scenario there are no ties. Only win/lose.

But it's amazing how much the odds change by adding the ties.

 

[SpicyMchaggis]

It's a large number.