What is the Pattern of Number Combinations and Sums When Extracting Digits?

[Stef Pieterse]

Hi
If i have many 3 digit number which are all different and can not be zero,and have to make as many 2 digit numbers from each one of them. They all give me 6 different 2 digit numbers.
What pattern will this follow in general? And what will the sums of the 2 digit numbers have in common?

I hope you can help me, thank you very much
Regards
Stef

 

[mnb96]

If I understood your question you are referring to http://en.m.wikipedia.org/wiki/Permutation?wasRedirected=true" of n objects, given by the factorial n!=n*(n-1)*...*1.

However how do you want to count the 2-digit numbers extracted from the 3-digit 111? Would you still count 6 or just 1?

You have to clarify what do you want to know specifically for the sum of two 2-digit numbers as I didnt get your point.

 

[ssd]

Suppose you have n digits and you are extracting r (=2 in your case) digits. Then nPr is the number of ways to get a r digited no.(since, all digits are different and nonzero). Then maximum of nCr different sums will be there and r! of the numbers will have a particular sum.