For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
02/11/2013

PROBLEM #1

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?

PROBLEM #2

What is the mean distance between two random points in a unit square?

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Problems from 01/31/13

PROBLEM #1

What 5-digit number has the following features:
If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.

SOLUTION 1
42857.

PROBLEM #2

There is one four-digit whole number n, such that the last four digits of n2 are in fact the original number n.

SOLUTION 2

9376.

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