**Source:**Alok Goyal Puzzle Page ( http://alokgoyal1971.com/ ) . Alok is ex-IIT Delhi, Partner at Helion VC

**Problem:**

__Part I (Easy):__Using a clock, divide a pizza among 12 people

__Part II (Difficult):__Using a clock, divide a pizza among 11 people?

Quant, Math & Computer Science Puzzles for Interview Preparation & Brain Teasing

A collection of ~225 Puzzles with Solutions (classified by difficulty and topic)

You’re trying to buy equipments whose costs are__ __appreciating. Item *i* appreciates at a rate of *r_i* > 1 per month, starting from $100, so if you buy it *t* months from now you will pay *100*((r_i)^t)*. If

you can only buy one item per month, what is the optimal order in which to buy them?

You’re trying to sell equipments whose costs are depreciating. Item *i* depreciates at a rate of *r_i* < 1 per month, starting from $100, so if you sell it *t* months from now you will get *100*((r_i)^t)*. If

you can only sell one item per month, what is the optimal order in which to sell them?

Airline check-in baggage has size restriction by so-called linear dimension: length + breadth + height should not exceed 62 inches. Prove that you can't "cheat" by packing a box with higher linear dimension into a box with lower linear dimension.

Prove that for any positive K and a natural number n, every (n*K)th number in the Fibonacci sequence is a multiple of the Kth number in the Fibonacci sequence.

More formally, for any natural number n, let F(n) denote Fibonacci number n. That is, F(0) = 0, F(1) = 1, and F(n+2) = F(n+1) + F(n). Prove that for any positive K and natural n, F(n*K) is a multiple of F(K).

The integers greater than zero are painted such that:

• every number is either gold or silver.

• both paints are used.

• silver number + gold number = silver number

• silver number * gold number = gold number

Given only this information, for each of the following decide whether it is a gold number, a silver number, or could be either:

1.) gold number * gold number

2.) gold number + gold number

3.) silver number * silver number

4.) silver number + silver number

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