   SEARCH HOME Math Central Quandaries & 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

01
02 or
04

1 extends to

10
12 or
14

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?

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.