Math CentralQuandaries & Queries


Question from Ayana:

What are all the possible four digit combinations using 0124. Please list them for me. Thank you.

Hi Ayana,

I assume that you don't want digits repeated. For example 1122 is not a "combination" you want. I'm going to call them "four digit strings" since combination is a technical word in mathematics. I'll show you how to list the four digit strings.

Start with the leftmost digit. You have four choices, 0, 1, 2 or 4.Now think about the next digit. Whichever digit you chose for the first digit you have three digits available to extend it to a two digit string. For example

0 extends to

02 or

1 extends to

12 or

and so on. How many two digit strings have you listed?

Whichever two digit string you have, you have two digits available to extend it to a three digit string. Write down all the possible three digit strings. How many are there?

Finally each of these three digit strings can be extended to a four digit string in only one way. Write them all down. How many are there?


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