Peter Bengtsson
secondary student

Can you help me find an equation for this correlation?

2*1+1
3*2+0
4*2+2
5*3+0
6*3+3
7*4+0
8*4+4
9*5+0
10*5+5

This is the way scores are calculated when you play the game Cascade. The more number of balls you manage to "click away", the better score you get. So, I wrote down lots of results for different amount of balls I clicked away. Clicking away one pair (two adjacent) of balls means 3 points. Clicking away three adjacent balls means 6 points. etc. You can see this from the list above.

What I now want to do is to find an equation with only ONE unknown! Y= kn*X+c or something. Whereby I only know X, I can find Y.

I am lost! How can this be done?? Can one use the Remainder Theorem for this? Any ideas?

Your numbers are

2*1+1 = 3
3*2+0 = 6
4*2+2 = 10
5*3+0 = 15
6*3+3 = 21
7*4+0 = 28
8*4+4 = 36
9*5+0 = 45
10*5+5 = 55

These are the number of ways to choose 2 objects from n+1 objects,  _(n+1)C₂. The value of  _(n+1)C₂ is (n+1)n/2.