## Saturday, July 29, 2006

### Bug split

A bug either splits into two perfect copies of itself or dies. If the probability of splitting is p (and is independent of the bug's ancestry), what is the probability that a bug's descendants die out?

Labels:
probability

## Sunday, July 16, 2006

### Weighing problem[S]

There are 101 coins among which one is counterfeit. we do not know whether the counterfeit coin is lighter or heavier ( than the rest of the coins ) which has to be determined within three weighings.how do you do it ?[S]

Labels:
general

## Saturday, July 15, 2006

### A problem from cryptography[S]

This field deals with converting plain text into cipher text ( un understandable ) using a mathematical construct to keep the information secure.A monoalplabetic substitution of +3 applied on the plain text "ram" gives cipher text "udp".Here 'mono alphabetic substitution' is the algorithm and '+3' is the key.

by knowing the algorithm but not the key can we retrieve plain text from cipher text ? [S]

by knowing the algorithm but not the key can we retrieve plain text from cipher text ? [S]

Labels:
code breaking

## Monday, July 10, 2006

### A simple inequality[S]

For real nums a,b,c prove that

(i) (a+b)(1/a +1/b)>=4

(ii)(a+b+c)(1/a +1/b +1/c) >=9

(iii) well, if this seems trivial prove in general for reals nums a_1,a_2,...a_n prove that

(a_1 +a_2 +...+a_n) (1/ a_1 +1/ a_2 +...+1/ a_n)>=n^2

(iv) well you may still go further proving (1+1/2 +1/3 +....) is not convergent.[S]

(i) (a+b)(1/a +1/b)>=4

(ii)(a+b+c)(1/a +1/b +1/c) >=9

(iii) well, if this seems trivial prove in general for reals nums a_1,a_2,...a_n prove that

(a_1 +a_2 +...+a_n) (1/ a_1 +1/ a_2 +...+1/ a_n)>=n^2

(iv) well you may still go further proving (1+1/2 +1/3 +....) is not convergent.[S]

Labels:
Inequalities

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