Happy Numbers

A happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digits.

To find a happy number, square the digits of a number and add them together giving a new number. Then square the digits of this new number and add them together. Repeat this prccess until the result becomes either number 4 or 1. If the result is 1, the original number is a happy number. If the result is 4 it is known as an unhappy or sad number.

The folowing example shows the process used to find if number 32 is a happy number:-

32 = 3² + 2² = 9 + 4 = 13;

13 = 1² + 3² = 10;

10 = 1² + 0² = 1² + 0² = 1;

As the resilts of the proces is 1, the number 32 is known as a happy number.

Example of an unhappy number:-

42 = 4² + 2² = 16 + 4 = 20;

13 = 2² + 0² = 4 + 0 = 4;

The number 42 is not a happy number as the process reults in number 4.

(c) Compiled by B V & T M Wood.

All rights reserved.

Disclaimer

To find a happy number, square the digits of a number and add them together giving a new number. Then square the digits of this new number and add them together. Repeat this prccess until the result becomes either number 4 or 1. If the result is 1, the original number is a happy number. If the result is 4 it is known as an unhappy or sad number.

The folowing example shows the process used to find if number 32 is a happy number:-

32 = 3² + 2² = 9 + 4 = 13;

13 = 1² + 3² = 10;

10 = 1² + 0² = 1² + 0² = 1;

As the resilts of the proces is 1, the number 32 is known as a happy number.

Example of an unhappy number:-

42 = 4² + 2² = 16 + 4 = 20;

13 = 2² + 0² = 4 + 0 = 4;

The number 42 is not a happy number as the process reults in number 4.

(c) Compiled by B V & T M Wood.

All rights reserved.

Disclaimer