# Puzzle 32) The Lucky Number

Submitted by Abhishek Jain, on October 01, 2017

Puzzle

Anuj, an intelligent boy discovers some new numbers named them as The Lucky Numbers. These numbers has the following special characteristics:

• They are of Four Digits.
• When number divided into two half’s that is, two digit on one side and remaining two on other side, then the square of sum of two half’s is equal to the original number.
• All the digits of the lucky number should be alike or different.

As an example, 3025 is a lucky number.The two half’s are 30 and 25.Thus, 30 added to 25 is 55, and 55 multiplied by 55 is 3025. Curious, is it not?

Now, Anuj needs your help to find another lucky number, composed of four figures, all alike, which may be divided from the middle and produce the same result.

9801

Explanation

The required Lucky Number is 9,801. If we divide this from the middle into two numbers and add them together we get 99, which, upon squaring give 9,801.

It is true that 2,025 may be treated in the same way, only this number is excluded by the condition which requires that no two figures should be alike.