For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
09/01/2010

PROBLEM # 1
A number of children are standing in a circle. They are evenly spaced and the 6th child is directly opposite the 19th child. How many children are there altogether?

PROBLEM #2
What is the area A of a cyclic quadrilateral (i.e., a simple quadrilateral that is inscribed in a circle, Fig. 1) with sides of length a, b, c, and d?

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Problems from 08/19/10

PROBLEM # 1

There are 9 balls. One of the balls is heavier than the rest, which all weigh the same. You have a balance. What is the least number of measurements it will take to find the heavier ball.

SOLUTION

PROBLEM #2

There are 9 balls. One of the balls is heavier or lighter than the rest, which all weigh the same. You have a balance. What is the least number of measurements it will take to find the ball which is different from the rest.

SOLUTION

3.

Congratulations to Kishore Balsara, Arul Prakash and Akshay Gowrishankar, who were winners of the last set of puzzles.

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Fig. 1