## Guess the number

Have an interesting puzzle? Let's hear it!

### Guess the number

Fairly simple, but I mentioned it in the "eyes" thread, so...

On a game show, two people are assigned whole, positive numbers. Secretly each is told his number and that the two numbers are consecutive. The point of the game is to guess the other number.

Here are the rules of the game:

–The two sit in a room which has a clock that strikes every minute on the minute
–The players cannot communicate in any way
–The two wait in the room until someone knows the other person’s number. They can guess at any time
–The game continues indefinitely until someone makes a guess
–The contestants win \$1 million if correct, and nothing if they are wrong

Can they win this game? If so, how?
WhoDatMath
Mathlete

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### Re: Guess the number

Does each person know that the other person has been told that the numbers are consecutive?

xander

xander
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Location: Sparks, NV, USA

### Re: Guess the number

Yes, it's mutual knowledge that the knowledge is mutual
WhoDatMath
Mathlete

Posts: 78
Joined: Thu Feb 10, 2011 4:53 pm

### Re: Guess the number

isn't it a fifty-fifty chance for the first, and 100% for the second?
Q.E.D. , or not?
Zapp
University

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Joined: Thu Feb 10, 2011 3:49 pm

### Re: Guess the number

The following relies on the assumption that the players will only leave when the clock chimes. Otherwise, the game is impossible.

Spoiler! :
Well, then. If my number is 1, I leave at the first minute, because I know that the other person can't have a lower number, and therefore has 2. If my number is 2, then I wait the first minute---either the other person will leave (they have 1) or they will stay (they have 3). Either way, I know their number. Continue this process by induction. My number is n, and I am still in the room at minute n, then the other person's number is n+1, and we can leave.

xander

xander
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Joined: Fri Feb 11, 2011 12:14 am
Location: Sparks, NV, USA

### Re: Guess the number

Lol...you're blending the problems. You don't have to leave the room, just announce the two numbers correctly. Your solution is correct. That's the strategy for the game. You'll always win.

If you leave the room, how can you collect your million dollars?
WhoDatMath
Mathlete

Posts: 78
Joined: Thu Feb 10, 2011 4:53 pm

### Re: Guess the number

WhoDatMath wrote:Lol...you're blending the problems. You don't have to leave the room, just announce the two numbers correctly. Your solution is correct. That's the strategy for the game. You'll always win.

If you leave the room, how can you collect your million dollars? :)

I was just responding to this line: "The two wait in the room until someone knows the other person’s number."

If I am waiting in the room, I want to leave, right? ;)

xander

xander
University

Posts: 154
Joined: Fri Feb 11, 2011 12:14 am
Location: Sparks, NV, USA

### Re: Guess the number

Yeah, it was awkwardly worded. I copy and pasted. Anyway, you got it right.
WhoDatMath
Mathlete

Posts: 78
Joined: Thu Feb 10, 2011 4:53 pm