From the set of numbers: {1, 2, 3, 4, 5, 6}, how many different sums can be formed by summing up any two numbers in the set?
I'm thinking this could be a permutation because 1+2 and 2+1 are not two different sums. So, =30.
Is this correct? Or would it be a combination...
Yes,
count combinations if you want the sums of different numbers,
but not if you want different answers!
If you add 2 adjacent numbers in your list,
they will equal the sum of the numbers that "flank" them,
ie 2+3=1+4, 3+4=2+5, 4+5=3+6
if a number has 2 numbers to the left and 2 numbers to the right,
you get (flanking 3)...2+4=5+1, (flanking 4)...3+5=6+2.
Flanking both 3 and 4...2+5=6+1
Hello, sfspitfire23!
From the set of numbers: {1, 2, 3, 4, 5, 6},
how many different sums can be formed by adding any two numbers in the set?
Assuming numbers can be repeated, we have this addition table:
. .
There are eleven different sums (2 through 12).
If numbers can not be repeated, we have this table:
. .
There are nine different sums (3 through 11).