**"Arithmetic"**

## Find the subsets

*By admin On April 6, 2012 · 2 Comments*

You are given a set of ‘n’ unique numbers. What is the maximum number of subsets that you can form such that if any two random subsets is chosen, they have exactly one element in common?

## Chameleon

*By admin On March 8, 2011 · 8 Comments*

At one point, a remote island’s population of chameleons was divided as follows:

- 13 red chameleons

- 15 green chameleons

- 17 blue chameleons

Each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.) Is it ever possible for all chameleons to become the same color? Why or why not?”

## Lake Monster

*By admin On January 31, 2010 · 2 Comments*

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can’t swim. He can run (along the perimeter) exactly 4x as fast as you can row, and he will always run towards the closest bit of shore to your boat. If two paths take him to this location equally quickly, he will arbitrarily choose one. If you can touch shore even for a second without the monster already being upon you, you can escape. The monster can reverse direction instantaneously and you can turn your boat instantaneously. Suggest a strategy that will allow you to escape, and prove that it works.

## Find the maximum & minimum!

*By admin On December 14, 2009 · 3 Comments*

This one is a simple algorithm question.

There are ‘n’ numbers. Maximum of the ‘n’ numbers can be found in (n-1) comparisons, similarly minimum can be found in (n-1) comparisons. In total there would be (2n-2) comparisons. Can you find out the maximum & minimum in lesser number of comparisons?

Ten people land on a deserted island. There they find lots of coconuts and a monkey. During their first day they gather coconuts and put them all in a community pile. After working all day they decide to sleep and divide them into ten equal piles the next morning.

That night [...]

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