Math and Logic Puzzles

[SleepyKrew]

Oh, I blame bad drawing. Good job Don.

[Max]

I just wrote a long response with pictures showing how Don was wrong.
But he's American. So his logic is kinda' correct.

Assuming the bus is not reversing or staying still that is.

[DonJosh]

Oh ya lol... I forgot about European driving laws XD

*Canadian, but whatever.

Should I go ahead with the next one?

[DonJosh]

Not accepting defeat, the hat-king sets up yet another challenge for his 100 wise men. He escorts them all into a dark room where half of the men are given red hats, while the other half are given blue hats. The room is pitch black, and no one can see anything. The king then tells them that he is standing next to a door. On the other side of that door is an illuminated room. The king challenges the men to enter the illuminated room one by one and form a line with all their hats alternating colour (Red, Blue, Red, Blue, Red, Blue, Red). However, once they are past the door, they may not return to the dark room, touch each other, or communicate in any way. The king gives the men time to devise a plan in the dark room. When eventually, much to his surprise, the men walk through the door one by one and form the line he challenged them to make. What was their plan?

[yabbaguy]

They all walk into the lit room, look at each other's hats, and stand in the proper order!

[DonJosh]

There is no communication allowed when in the illuminated room. Also, they enter the room one by one.

[yabbaguy]

They have to line up in the order they enter?

[DonJosh]

No.

[KageLord]

No.

So why doesn't yabba's solution work?

[yabbaguy]

The plan is seriously "walk in together and count everyone else's hat". If I'm one of those guys, I walk in and see 49 blue and 50 red hats. I know instantly what hat I have. Same said for every single person in the room. Then assemble the line for the win.

[DonJosh]

-.- Hm. I must've gotten the question wrong.
Since thats not the answer I'm looking for, lets assume it doesnt work, and reset the guess count to 0.

[yabbaguy]

Oh - how about this. Maybe the rule is that they have to always be in a line at all times.

RULE: If you see like-colored hats on two adjacent people, barge in between them. If no such groupings exist, you can stand anywhere (let's just say the back of the line).

So I walk in and see RRRB. I'm just going to walk in between two Rs.

RR

R

RB. Oops, I made the situation worse. But there are more Bs than Rs, so eventually that will get plugged up. Say it eventually gets like this:

[RBRBRBR...B]RRRR with 4 Bs remaining. Bs have three points they need to intervene at to split the RRRR chunk, and the remaining B goes to the end and is before an R.

success.

[DonJosh]

^ correct

[yabbaguy]

Haven't had an expected value question... ever, have we?

After seeing yabbaguy plug his stupid game which goes on about the same crap about colorful spheres and other mathematical bullshit, you've had enough of him spamming every Mish Mash thread about it. You complain to him and he promises you that if you can solve a mathematical puzzle about it, he'll shut up about it. Maybe.

To win $500K, a main player has to confront 5 other players. Each player will generate a random number from 0-4 inclusive, each digit being equally likely to show. If this random digit is anything other than a 0, it's a "win", and a 0 constitutes a "loss".

The main player wins money as follows, for 0-5 wins: $0, $1000, $10K, $25K, $100K, $500K. What is the expected cash value to the player?

[Max]

£4538 (rounded to nearest pound)?

[Max]

EBWOP.

Foolish me I did some stuff the wrong way round...

£210,438 Again to the nearest pound.

So I think I've probably made a grave error in my calculations.

[StrangerCoug]

You're only allowed one shot, Max.

I think I have the way to compute this down pat; I just need the odds of each win.

[SleepyKrew]

Does not Compute

[Max]

You're only allowed one shot, Max.

I think I have the way to compute this down pat; I just need the odds of each win.

Binomial Distribution is the best route for this.

[StrangerCoug]

I know.

[yabbaguy]

You're only allowed one shot, Max.

I think I have the way to compute this down pat; I just need the odds of each win.

:badposting:

1. He's given the correct answer. Why should we deny him the victory now that the puzzle's answer is in plain sight? I wish this was less of a moderated contest with rules and more just us showing off/guessing for fun. People who multi-guess just to be jerks are... jerks, but I don't approve of this rule, esp. considering Max made a simple error - maybe inverting his .2s and .8s the wrong way around? I haven't checked.
2. You know the odds of each win - it's .8 . You've seen the actual show, it's a target of 0. 1-4 win, 0 doesn't.

I could zing him on the illegal exchange of currency though.

[StrangerCoug]

The reason I disallow multiple guesses is to allow other people a chance at it.

[yabbaguy]

So I guess whoever arrives at the actual solution wins then. Has to be, you all know the answer already.

[Max]

esp. considering Max made a simple error - maybe inverting his .2s and .8s the wrong way around?

I could zing him on the illegal exchange of currency though.

That was my error. I was thinking that was a bit low. xD

[StrangerCoug]

Max, up to you.