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Assume that the question is really looking for an "odd" number, (not an "old" number).

Then it's [ 1001 ].

Q: What is the least four digit old number where repetition of the digit is allowed?

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1,023

least two-digit composite number = 11

Even number are those that can be divided by 2.First 4-digit number is 1000 but this is not oddSo, the least 4-digit odd number is 1001

123456789

One hundred is the least three-digit square number. It is formed by 102.

Related questions

1,023

Without repetition or leading 0s, it is 1023

4 is the least one digit composite number

least two-digit composite number = 11

10 is the smallest 2 digit number.

Even number are those that can be divided by 2.First 4-digit number is 1000 but this is not oddSo, the least 4-digit odd number is 1001

123456789

One hundred is the least three-digit square number. It is formed by 102.

The number 8 in that question is the number with the least amount of value (0.008).

4

6

997 is the last 3 digit prime number