Calculate how many possible sets there are in a set game

set.R

#Calculate how many sets there are in a set game.
 

#each card has 4 characteristics with 3 factors each
color <- c("red", "green", "purple")
shape <- c("round", "diamond", "curly")
texture <- c("fill", "empty", "striped")
number <- c("one", "two", "three")

create_board <- function(n = 12){
  data.frame(color = sample(color, n, TRUE),
             shape = sample(shape, n, TRUE),
             texture = sample(texture, n, TRUE),
             number = sample(number, n, TRUE))  
}

set <- function(a = c(1,2,3), d){ #a = position in the board; d = board
  ifelse(all((d[a,1] == d[a[1],1]) | all(c(d[a[2:3],1] != d[a[1],1], d[a[2],1] != d[a[3],1]))) &
           (all(d[a,2] == d[a[1],2]) | all(c(d[a[2:3],2] != d[a[1],2], d[a[2],2] != d[a[3],2]))) &
           (all(d[a,3] == d[a[1],3]) | all(c(d[a[2:3],3] != d[a[1],3], d[a[2],3] != d[a[3],3]))) &
           (all(d[a,4] == d[a[1],4]) | all(c(d[a[2:3],4] != d[a[1],4], d[a[2],4] != d[a[3],4]))), 
         TRUE, FALSE)
} 

any_set <- function(d, n = 12){ #n can be derived from d, and simplify one param.
  x <- c()
  cb <- combn(x = n, m = 3, simplify = TRUE) #220 combinations for n = 12
  for(i in 1:ncol(cb)){
    x[i] <- set(cb[,i], d)
  }
  cb[,which(x)]
}

#example with a random game
d <- create_board()
any_set(d)

#one practical example
d <- data.frame(color = c("v", "m", "r", "v", "v", "m", "r", "m", "m", "m", "m", "v"),
                shape = c("c", "r", "c", "r", "r", "r", "o", "o", "c", "r", "r", "r"),
                texture = c("h", "h", "h", "s", "r", "h", "h", "r", "r", "s", "r", "r"),
                number = c("1", "3", "2", "1", "3", "2", "2", "1", "1", "2", "3", "1")) 
any_set(d)

#how many non-sets are in 100 games?
x <- c()
for(i in 1:100){
  x[i] <- ifelse(sum(any_set(create_board())) > 0, 0, 1)
} #slow, which means code can be optimized.
sum(x) #5 to 9 games with no sets on average.