 181
 2
Hello guys, i have a unique problem to solve.
Let's imagine you're playing a board game similar to Risk. The game can be played by anywhere from 2 to 22 players, and the game board will be resized accordingly based on the number of players. The board also wraps, so edge provinces connect to the province on the opposite end. This game also has one additional concept: For each player that is in the game, the game board has an additional resource province. These provinces need to be equidistant to all nearby players (for the purposes of fairness). If necessary, the board can have more resource provinces than the number of players, as long as the distribution is fair. The board should also be as close to square as possible. Rectangles are okay, as long as they are not too long and skinny.
Typically, the game board will have 16 provinces per player. For example, here's a drawing of a 4 player game board.
If we divided this into quarters, all 4 quarters would be the same. The green spots denote player starts, the pink spots denote the resource locations. Note that the resources are always placed equidistant from all players, and all players are placed equidistant to other players and resources. In short, this can be considered a fair layout since every player has the exact same starting conditions.
Now, what if we had 5 players? This makes it more difficult to create a similar layout. Fortunately with a little thinking, i came up with:
It's not ideal... There are 6 resource provinces for 5 players, and we had to bend the 16 provinces per player rule to accommodate 5 players. Still, it is pretty close to being fair. Every player has 2 resource provinces within 2 moves from their start position. The reality is that we need to bend the rules for cases such as this. As long as there are roughly 16 provinces per player, and at least 1 available resource province for each player, it is fine.
I have managed to solve this problem for the simple cases, but i am left with difficult cases now: 7, 10, 11, 13, 14, 17, 18, 19, 21, 22
It's worth mentioning again that we want to avoid layouts that are too rectangular. For 10 players, it is tempting to make make a layout consisting of 2 rows of 5 players. Unfortunately this layout is too rectangular, we want our map to be as square as possible.
If anyone could help me come up with layouts for the difficult cases i would be most grateful!
Let's imagine you're playing a board game similar to Risk. The game can be played by anywhere from 2 to 22 players, and the game board will be resized accordingly based on the number of players. The board also wraps, so edge provinces connect to the province on the opposite end. This game also has one additional concept: For each player that is in the game, the game board has an additional resource province. These provinces need to be equidistant to all nearby players (for the purposes of fairness). If necessary, the board can have more resource provinces than the number of players, as long as the distribution is fair. The board should also be as close to square as possible. Rectangles are okay, as long as they are not too long and skinny.
Typically, the game board will have 16 provinces per player. For example, here's a drawing of a 4 player game board.
If we divided this into quarters, all 4 quarters would be the same. The green spots denote player starts, the pink spots denote the resource locations. Note that the resources are always placed equidistant from all players, and all players are placed equidistant to other players and resources. In short, this can be considered a fair layout since every player has the exact same starting conditions.
Now, what if we had 5 players? This makes it more difficult to create a similar layout. Fortunately with a little thinking, i came up with:
It's not ideal... There are 6 resource provinces for 5 players, and we had to bend the 16 provinces per player rule to accommodate 5 players. Still, it is pretty close to being fair. Every player has 2 resource provinces within 2 moves from their start position. The reality is that we need to bend the rules for cases such as this. As long as there are roughly 16 provinces per player, and at least 1 available resource province for each player, it is fine.
I have managed to solve this problem for the simple cases, but i am left with difficult cases now: 7, 10, 11, 13, 14, 17, 18, 19, 21, 22
It's worth mentioning again that we want to avoid layouts that are too rectangular. For 10 players, it is tempting to make make a layout consisting of 2 rows of 5 players. Unfortunately this layout is too rectangular, we want our map to be as square as possible.
If anyone could help me come up with layouts for the difficult cases i would be most grateful!
Attachments

26.2 KB Views: 86

59.1 KB Views: 85