Another Logic Puzzle

[durron597]

Great answers from everyone. However, there is still some depth to this problem that has been overlooked; if you can answer the question:

Also can you generalize? What would happen if A's number was 136, B's number 221, and C's number 357?

You most likely will have realized what is really going on here.

[sirio11]

[ QUOTE ]
Also can you generalize? What would happen if A's number was 136, B's number 221, and C's number 357?


[/ QUOTE ]

I don't understand what do you mean by what would happen?

[durron597]

In other words, A says "I don't know". B says "I don't know". Then C, then A, etc. etc. etc. until one of them figures it out. How many times until that occurs with those three numbers, if ever?

[hobbsmann]

Initially C knows his number is either A+B or B-A and once A and B say they don't know then he knows he has the largest number of the three and thus 357. Once A knows that C knows his own number then A knows that his number is C-B or 136 and finally B knows his number is 221. <font color="white"> </font>

[durron597]

[ QUOTE ]
Initially C knows his number is either A+B or B-A and once A and B say they don't know then he knows he has the largest number of the three and thus 357. Once A knows that C knows his own number then A knows that his number is C-B or 136 and finally B knows his number is 221. <font color="white"> </font>

[/ QUOTE ]

Wrong.

[PairTheBoard]

[ QUOTE ]
In other words, A says "I don't know". B says "I don't know". Then C, then A, etc. etc. etc. until one of them figures it out. How many times until that occurs with those three numbers, if ever?

[/ QUOTE ]

From sirio11's proof, it looks like it works for any three integers where B=(3/2)A AND A+B is not divisible by 4.

PairTheBoard

[durron597]

Clearly those two conditions are not true in my second set of #s.

[PairTheBoard]

durron --
"Also can you generalize? What would happen if A's number was 136, B's number 221, and C's number 357?"

[ QUOTE ]
[ QUOTE ]
In other words, A says "I don't know". B says "I don't know". Then C, then A, etc. etc. etc. until one of them figures it out. How many times until that occurs with those three numbers, if ever?

[/ QUOTE ]

From sirio11's proof, it looks like it works for any three integers where B=(3/2)A AND A+B is not divisible by 4.

PairTheBoard

[/ QUOTE ]

durron --
"Clearly those two conditions are not true in my second set of #s."

Oh. I see what you mean. They might keep going around saying they don't know numerous times before possibly reaching a conclusion. With the numbers 136,221,357 once C says he doesn't know ... then I guess what happens is I say I don't know.

PairTheBoard

[durron597]

[ QUOTE ]

Oh. I see what you mean. They might keep going around saying they don't know numerous times before possibly reaching a conclusion.

[/ QUOTE ]

Yes. This is exactly what will happen (and for those numbers, they will reach a conclusion).

[durron597]

Bump.