   SEARCH HOME Math Central Quandaries & Queries  Question from Theresa, a parent: I need to know the number of 4 digit numbers that can be formed using 1-2-3-4 without repeating numbers Hi Theresa,

How many 2 digit numbers that can be formed using 1-2 without repeating numbers?

The answer is clearly 2. The numbers are 12 and 21.

How many 3 digit numbers that can be formed using 1-2-3 without repeating numbers?

Each of the two, 2 digit numbers can be turned into a three digit number by adding the 3 before the two digits, between the two digits or after the two digits. For example 12 generates 312, 132 and 123. Hence there are 3 times as many three digit numbers as two digit numbers. Thus the number of three digit numbers is 3 × 2 = 6.

How many 4 digit numbers that can be formed using 1-2-3-4 without repeating numbers?

Each of the six, 3 digit numbers can be turned into a four digit number by adding the 4 before the three digits, between the first and second digits, between the second and third digits or after the three digits. Hence there are 4 times as many four digit numbers as three digit numbers.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.