Brain teasers n Math Puzzles

[vivek joshi]

This thread is specifically for math lovers. I am posting two questions as a start, one pure math based and the other Strategy based:

1. A man has a stick. He breaks it randomly into 3 pieces. What is the probability that the 3 pieces can form a triangle?

2. P and Q are two perfect strategists and they have a mutual friend R

    R has two numbers with him: a and b

   R tells both P and Q  that 1<a<b and a+b<=100

    He tells the value of a*b to Q only

          and the value of a+b to P only

    P and Q are not allowed to share their values with each other. So they decide to have following conversation. Based on this conversation determine the value of a and b

    (Use of computer is allowed to solve this problem)

    Q -> I cannot determine a and b

    P -> I already know that

    Q -> Now I can determine a and b

    P -> So can I

[Jyoti.Pks]

for the first it will be 3

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[vivek joshi]

It is probability, it has to be less than 1. Do you mean 3% or 1/3?

[Tomasz Klimczak]

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I think the answer for q1 is 1. Am I right. If so I will reward myself with a glass of orange juice.

Cheers,

Tomek

[Jyoti.Pks]

 it wil be 1/3 % 

[Jyoti.Pks]

 it wil be 1/3 %  for a particular trianlge.also it is not mention any triangle type so it  will for 3/3%