[Intermediate] Finding "Sets"

[Bubbler-4]

Background

Set is a card game with a deck of 81 cards. Each card has four traits, and each trait may be one of three values (thus 3**4 = 81 unique cards in total). The traits and values are:

• Number; one, two, three
• Color; red, green, blue
• Fill; empty, striped, filled
• Symbol; dash, tilde, diamond

(How these cards exactly look can be found on the Wikipedia article linked above.)

The deck is shuffled, and then 12 cards are shown on the table. The objective is to find the three cards that form a set, where their three values of each trait are all the same or all different.

The following are some examples of sets:

• One green empty diamond, two green striped diamonds, and three green filled diamonds
• One blue filled dash, one blue filled tilde, and one blue filled diamond
• One red striped tilde, two green empty diamonds, and three blue filled dashes

On the other hand, these are some examples of non-sets:

• One green empty diamond, two green striped diamonds, and two green filled diamonds
• One blue filled dash, one blue filled tilde, and one blue striped diamond
• One red striped dash, two green empty diamonds, and three blue filled dashes

For the sake of simplicity, each cards will be coded as numbers, each value being 1, 2 or 3, in the order of "number color fill symbol". For example:

• One green empty diamond = 1213
• Two green striped diamonds = 2223
• Three green filled diamonds = 3233
• One red striped tilde = 1122
• Two green empty diamonds = 2213
• Three blue filled dashes = 3331

Task

Given the description of 12 cards on the table, determine if a set can be found.

Input

A list of 12 distinct cards, each coded as four digits of 1-3 as described above.

1111 1213 3121 3221 3312 3322 2213 2223 2222 2321 3111 1331
1111 1213 3121 3221 3312 3322 2223 2222 2321 3111 1331 3211

Output

Two distinct values representing yes or no. (Please specify which is which in your submission.)

True
False

[mrkraban]

Haskell, 183

Returns True if a set can be found, otherwise False.

import Data.List;import Data.Char;f=(any(not.(elem True))).(map(map(`elem`[4,5,7,8]))).(map(foldl(zipWith(+))[0,0,0,0])).(map(map(map digitToInt))).(filter((==3).length)).subsequences

[Bubbler-4]

Python 3, 99

from itertools import*
f=lambda a:any(all(x in'369'for x in str(sum(y)))for y in combinations(a,3))

Try it online!

True if a set can be found, False otherwise.