1. ## combinatorics

The set {0, 1, 2, 3) is given. The only operation on the group is addition.

ff the result of the addition operation is one items of the set, it called internal result,
else it called external result.

The internal result is 4
The external result is 6.

How I represent it by representation of combinatorics:
(1) The number of internal result?
(2) The number of external result?
(3) The number of result that are derive by commutative law?

2. ## Re: combinatorics

How are you counting "results"? For example, 0+ 3= 3 and 1+ 2= 3. Is that one "result" or two? Do you count 3+ 0 and 2+ 1 as different? If you really meant to count "results" there would be 4 "internal results" because there are 4 numbers in {0, 1, 2, 3}.

In any case, it is very easy to list all possible sums and determine whether they are "internal" or "external". If you mean to count 0+ 3 and 1+ 2 as different "results" then you are counting 0 +0, 0+ 1, 0+ 2, 0+ 3, 1+ 1= 2, and 1+ 2: 5 "internal results". For "external results" we have 1+ 3= 4, 2+ 2= 4, 2+ 3= 5, and 3+ 3= 6. Four "external results". If by "derived by commutative law" you mean to count 1+ 3 as different from 3+ 1, just double every result except 0+ 0, 1+ 1, 2+ 2, and 3+ 3.

3. ## Re: combinatorics

O.K. I count the number of exercises...
The number of exercise with internal result is 4.
The number of exercise with external result is 6.

What are the formulas of:
(1) The number of exercise with internal result?
(2) The number of exercise with external result?
(3) The number of exercise that satisfed the commative law?

4. ## Re: combinatorics

Originally Posted by policer
The set {0, 1, 2, 3) is given. The only operation on the group is addition.

ff the result of the addition operation is one items of the set, it called internal result,
else it called external result.

The internal result is 4
The external result is 6.

How I represent it by representation of combinatorics:
(1) The number of internal result?
(2) The number of external result?
(3) The number of result that are derive by commutative law?
@policer, It would be a tremendous help to us and ultimately to you if you could get someone to help you with translations. This thread is a perfect example of that. There are at three of the regulars who have vast experience in this type problem. This problem has potential for being quite interesting. But the fact of your limited facility in English means that none here knows what you mean. Therefore, you have hurt yourself.