4 digit number knowing one number

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In summary, the conversation discusses how to determine the number of possible 4-digit numbers when one digit is known but its placement is unknown. The solution involves considering the four possible positions for the known digit and multiplying it by the number of ways the remaining three digits can be arranged. It is assumed that 0 cannot be the first digit.
  • #1
annenap
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I can't get started on this. If I am trying to figure out a 4-digit number, and I know one of the numbers, but not which digit it is, how many possible numbers are there?
Thanks!
 
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  • #2
Welcome to PF.
The trick is to think of it like this: you have four slots which can take a single digit each - the four digits make one number.

There are four possible places that the known digit can be in.
So the answer must be four times the number of ways that the remaining three digits can be arranged.
There are 10 possible digits.

Presumably you have just been doing permutations and combinations?
 
  • #3
annenap said:
If I am trying to figure out a 4-digit number,
and I know one of the numbers [digits], but not which digit it is,
how many possible numbers are there?

I have questions.

Is this digit you know different from all of the other digits?



You are not allowing 0 for a first digit?
 

1. What is a 4 digit number?

A 4 digit number is a number that contains four digits, with each digit representing a value from 0-9. For example, 1234 is a 4 digit number.

2. How many different 4 digit numbers are there?

There are 10,000 different 4 digit numbers. This can be calculated by multiplying 10 possible values for each digit (0-9) by itself four times (10 x 10 x 10 x 10 = 10,000).

3. If I know one digit of a 4 digit number, can I determine the other three digits?

No, knowing one digit of a 4 digit number does not provide enough information to determine the other three digits. Without any other context or constraints, there are still 1,000 possible combinations for the remaining three digits.

4. Can a 4 digit number start with a 0?

Yes, a 4 digit number can start with a 0. However, if the number is used to represent a quantity, the leading 0 is typically dropped. For example, 0123 would be written as 123.

5. How are 4 digit numbers used in science?

4 digit numbers are used in science to represent quantities, measurements, and data. They can also be used in mathematical calculations and statistical analysis.

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