Proof: Let’s assume there are finite number of prime numbers. Then let the greatest prime number is N.

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# Category: Concrete Mathematics

# Prove that, there are infinite number of prime numbers.

# How many regions do N lines divide a plane?

### Explanations:

# The Josephus Problem

### Introduction

# The Tower of Hanoi Solution

### Definition:

Proof: Let’s assume there are finite number of prime numbers. Then let the greatest prime number is N.

Continue reading “Prove that, there are infinite number of prime numbers.”

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**N** straight lines are drawn on a plane paper. Each line intersects with rest all lines. That means **N**‘th line intersects **N-1**lines. You can assume infinite number of lines can be drawn on that paper. You have to find total regions after **N** lines are drawn. An image is given below to understand the problem clearly.

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The **Josephus Problem** is a count-out game which is regarded as a theoretical problem in Computer Science or Mathematics. In this game, **n** people stand in a circle **s** is the starting number of people. **s** is holding a sword where **s**kills **s+k-1**‘th people from his position and gives his sword to **s+k**‘th people. Thus **s+k** becomes new **s**. Going in the same direction this procedure is repeated until one person is left. Remaining one person is marked as a winner.

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The Tower of Hanoi problem is a puzzle which can be solved by mathematically and can be implemented in programming code as well. The tower is also called **Tower of Brahma** or **Lucas’ Tower**. In this, game there are three pegs and one one of them hold **n** disks. **n** disks are ordered from higher radius to lower radius from the bottom to top.

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