What are the first 10 decimal digits in the decimal representation of the fractional part of ?
Note: The fractional part of a non-negative real number is the part of the number that appears after the decimal point.

## Monthly Archives for March, 2013

## Setting an exam paper

There's a class of 60 students taking a class. The professor wants to give a lot of flexibility to the students in choosing their final exam paper. Each student must list 6 topics of his/her choice. Further, he must declare one of 2 different days on which he wants to take the finals. The professor has exactly 1 question per topic. The professor is free …

**Continue reading the story**"Setting an exam paper"## Zebra crossing river

A zebra was going to the river. On the way the zebra encountered five giraffes. Each giraffe had five monkeys on their neck. How many animals were going to the river?
via Brain Teasers.
Answer:
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
Just one - the zebra. The other 30 animals (5 giraffes and 25 monkeys) were going the other way.

## Weighing coins

There are nine coins, one real and eight fake. Four of the fake coins weigh the same and are lighter than the real coin. The other four fake coins weigh the same and are heavier than the real coin. Find the real coin in seven weighings on the balance scale (In fact, it is possible to do so in only 6 weighings).
- via Tanya's …

**Continue reading the story**"Weighing coins"## Sampling uniformly at random from a stream

Suppose is a stream of objects. The goal is to produce a stream such that at each time , is uniformly distributed among . However you are allowed to use only memory. How can this be achieved?
Hint: You don't have to make 's independent of each other.
-- Via prof. Ashish Goel's class on randomized algorithms.

## Chocolate blocks

You are given an m×n block of chocolate which you wish
to break into mn unit squares. At each step, you may
pick up one piece of chocolate and break it into two pieces
along a straight line. What is the minimum number of
steps required?
via Australian Mathematical Society

## Graphing equations

This series of puzzles attempt to develop intuition regarding graphing equations.
First question: Plot the curve . Guess it's shape intuitively. Hint: .
Second question: Plot the 3-d surface . Hint: Use the first question.
Third question: Plot the 3-d surface
via prof. Ernst Boyd, an amazing lecturer and a juggler.