For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
09/10/2010

PROBLEM # 1

What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225

PROBLEM #2
An ant and a blind spider are on opposite corners of a cube. The ant is stationary and the spider moves at random from one corner to another along the edges only. What is the expected number of turns before the spider reaches the ant?

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Problems from 09/02/10

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?

SOLUTION

26.

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?

SOLUTION

A= sqrt((s-a)(s-b)(s-c)(s-d)), where s=(a+b+c+d)/2.

Congratulations to Arun Lahori, Nupur Parikh, Sudha Godhani Patel and Deepa Fernandes Prabhu, who were winners of the last set of puzzles.

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