If anyone doesn't know the rules for catch 21, it is a game played with 1 regular deck of cards where the goal is to score the most points by creating groups of cards that = 21 exactly. You draw one card at a time that you can place into any of 4 piles, as long as it will not cause the pile to increase past 21. You can discard, however you can not touch the discarded cards once they are discarded. Groups can have up to 5 cards. Once 21 or 5 cards is reach, the cards are taken away.
Anyway, I am trying to figure out a way to make a cheat sheet.
2 cards : [10,A] [J,A] [Q,A] [K,A] 3 cards : ??? 4 cards : ??? 5 cards : ???
My question is: How do I go about finding all the possible groupings that add to 21 with 3 cards, 4 cards, and 5 cards? like x+y+z=21 ; x,y,z <_ 11 but also paying respect to the 4 of each card limit set by the standard deck of cards.
Any help would be great, Thank You!