Question

I am the smallest 4digit number that remains the same even when written in the reverse order.what number am i

Answer 1

You're 1001.

You said you remain the same even when you're written in the reverse order.

Also you said you're the smallest 4 digit number.

Let me take you decimally as a/b/c/d. (Decimally means to write a number by splitting the terms. In a/b/c/d, the digits are a, b, c, d and they're split by slash /)

You'll be d/c/b/a when written in reverse order.

As you said that you remains same in reverse order,  a = d  and  b = c.

The lowest possible value for a = d can't be 0, because you won't be a four digit number, will you?

Thus a = d = 1, isn't it?

And the lowest possible value for b = c is 1, thus b = c = 1.

Thus  you're 1001.

If you were the smallest 2 digit number, then you would be 11.

If you were the smallest 3 digit number, then you would be 101.

If you were the smallest 5 digit number, then you would be 10001.

If you were the smallest 6 digit number, then you would be 100001.

If you were the smallest 'n' digit number, then you would be '10ⁿ⁻¹ + 1'.

Answer 2

Answer:

1001

Explanation:

• We know that the smallest four digit number is 1000.
• But if we write this number in reverse order, it will become 0001 which is not same as 1000.
• The next four digit number is 1001 and if we write this number in reverse order, we again get

                                           1001.

Hence the smallest four digit number which does not change when written in reverse order is

1001.