(A) Out of 100 straight lines having respective lengths 1, 2, 3, ......, 99, 100; determine the total number of ways in which four straight lines may be chosen which will form a quadrilateral in which a circle may be inscribed.

(B) Out of 101 straight lines having respective lengths 1, 2, 3, ......, 99, 100, 101; determine the total number of ways in which four straight lines may be chosen which will form a quadrilateral in which a circle may be inscribed.

(In reply to start of analysis; computer finish (spoiler) by Charlie)

Just verifying:

The addition of 101th line causes additional 4-tuples from (1,2,100,101) to (98,99,100,101).

Simple count shows that we add (49,49,48,48,....1,1) new combinations.

49*50=2450  
so does  82075-79625=2450

Just verifying!

Posted by Ady TZIDON on 2010-06-29 10:52:04