## Saturday, 2 July 2016

### Playing with numbers!

My love for numbers has made me write this one. MS Excel and the phenomena of reconciliation of anything and everything has increased my liking for numbers very much.
Still I admit I'm not the master of it and hence this blog post to get a understanding of it by you and me.

Riddle: Three Guys at A Hotel

Three guys rent a hotel room for the night. When they get to the hotel they pay the INR 3000 fee, then go up to their room. Soon the bellhop brings up their bags and gives the guys back INR 500 because the hotel was having a special discount that weekend. So the three guys decide to each keep INR 100 of the INR 500 and to give the bellhop a INR 200 tip. However, when they sat down to tally up their expenses for the weekend they could not explain the following details:

Each one of them had originally paid INR 1000 (towards the initial INR 3000), then each got back INR 100 which meant that they each paid INR 900. Then they gave the bellhop a INR 200 tip. However, 3 * 900 + 200 = INR 2900.

The guys couldn't figure out what happened to the other INR 100. After all, the three paid out INR 3000 but could only account for INR 2900.

Can you determine what happened?

It all boils down to the fact that their math is incorrect.

They did NOT spend INR 900 * 3 + 200.

If the guys get INR 300 back and each takes INR 100. Then they spent exactly INR 2700. INR 2500 for the room and INR 200 for the tip. Remember they got exactly INR 300 in total back.

Number types:

Numbers can be classified according to how they are represented or according to the properties that they have.

Main types:

Natural numbers:
The counting numbers {1, 2, 3, …}, are called natural numbers.

Whole numbers:
The numbers {0, 1, 2, 3, …}.

Integers:
Positive and negative counting numbers, as well as zero:{…, -2, -1, 0, 1, 2,…}.

Rational numbers:
Numbers that can be expressed as a ratio of an integer to a non-zero integer. All integers are rational, but the converse is not true.

Real numbers:
Numbers that have decimal representations that have a finite or infinite sequence of digits to the right of the decimal point. They can be positive, negative, or zero. All rational numbers are real, but the converse is not true.

Irrational numbers:
Real numbers that are not rational.

Imaginary numbers:
Numbers that equal the product of a real number and the square root of –1. The number 0 is both real and imaginary.

Complex numbers:
Includes real numbers, imaginary numbers, and sums and differences of real and imaginary numbers.

Hypercomplex numbers include various number-system extensions: quaternions, octonions, sedenions, tessarines, coquaternions, and biquaternions.

Number representations:

Decimal:
The standard Hindu–Arabic numeral system using base ten.

Binary:
The base-two numeral system used by computers.

Roman numerals:
The numeral system of ancient Rome, still occasionally used today.

Fractions:
A representation of a non-integer as a ratio of two integers. These include improper fractions as well as mixed numbers.

Scientific notation:
A method for writing very small and very large numbers using powers of 10. When used in science, such a number also conveys the precision of measurement using significant figures.

Knuth's up-arrow notation and Conway chained arrow notation:
Notations that allow the concise representation of extremely large integers such as Graham's number.

Types of integer:

Even and odd numbers:
An integer is even if it is a multiple of two, and is odd otherwise.

Prime number:
An integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ….

Composite number:
A number that can be factored into a product of smaller integers. Every integer greater than one is either prime or composite.

Polygonal numbers:
These are numbers that can be represented as dots that are arranged in the shape of a regular polygon, including:
Triangular numbers, Square numbers, Pentagonal numbers, Hexagonal numbers, Heptagonal numbers, Octagonal numbers, Nonagonal numbers, Decagonal numbers, and Dodecagonal numbers.

There are many other famous integer sequences, such as the sequence of Fibonacci numbers, the sequence of factorials, the sequence of perfect numbers, and so forth.

Refer for more: https://en.m.wikipedia.org