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### Scoring Question

AuthorMessage
Goober
27-05-2007 19:34:11
When two groups of campers are combined, how does the scoring work?

In game 3079, turn 29, why did I get 20 points?

Thank you.
guyhill
27-05-2007 19:37:34
When you combine 2 groups, the additional amount of points is (m+1) * (n+1), where m is the size of one of the groups and n is the size of the other.

Example: combine a group of 2 with a group of 3 into a group of 6 caravans.

Score before the join = 3 (1+2) points + 6(1+2+3) points = 9 points
Score after the join = 1 + 2 + 3 + 4 + 5 + 6 = 21 points.
Difference = 12 points = (2+1) * (3+1).

Hope this helps. If you want I can send you the full proof.

Just for fun: when joining 3 groups you gain (m+1) * (n+1) * (k+1) - m*n*k points.
Cwali
27-05-2007 20:32:54
That answer is right. But I want to answer in an other way:
You get the points for the groups and for the lakes (number of ships) when all spaces are occupied. So the points you see at your name when you do a move are only to help, you don't have to remember or write during the game and the points for the lakes you can loose later.
The groups, when all spaces are occupied, count this way:
1 single camper: 1 point
2 connected campers: 3 points
3 connected campers: 6 points
4 connected campers: 10 points
5 connected campers: 15 points
6 connected campers: 21 points
7 connected campers: 28 points
8 connected campers: 36 points
9 connected campers: 45 points
10 connected campers: 55 points
11 connected campers: 66 points
12 connected campers: 78 points
13 connected campers: 91 points
14 connected campers: 105 points
15 connected campers (it happens): 120 points
and so on.
guyhill
27-05-2007 21:30:58
In other words, n * (n+1) / 2, where n is the number of campers in a group.

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