Question

Who am I?

I am a 4-digit number.

In my number there are only two different digits.

The sum of all my digits is 6.

My hundreds digit is less than 2.

My tens digit is even.

The order of my digits is least to greatest.

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Answer 1

Given:

A 4 digit number.

There are only 2 different digits.

Sum of all digits = 6

Hundredth place digit < 2

Tenth place digit is even.

Order of digit is least to greatest.

To Find:

Since there are only 2 different digits, Let the digits be a , a , b , b .

Where b > a

Now, its given that,

• Sum of digits =6
• 2a+ 2b = 6
• a + b = 3

Therefore a  can be a ∈ { 0,1}

and b can be b ∈ { 2,3} , as 0+ 3 = 3 and 1+2 =3

Since order of the digits is from least to greatest a cannot be 0, since if 0 comes at 1000s place, the number will be a 3 digit instead of 4 digit.

Therefore,

• a = 1
• b = 3 -1 = 2

Now the number can be 1122.

Given hundreds digit is less than 2.

• In 1122 , Hundreds digit is 1. Hence verified.

Also Tens digit is even.

• In 1122 tens digit is 2, even number. Hence verified.

Therefore the 4 digit number is 1122.