# Set, the card game

Set, the card game
You are encouraged to solve this task according to the task description, using any language you may know.

The card game, Set, is played with a pack of 81 cards, each of which depicts either one, two, or three diamonds, ovals, or squiggles. The symbols are coloured red, green, or purple, and the shading is either solid, striped, or open. No two cards are identical.

In the game a number of cards are layed out face up and the players try to identify "sets" within the cards.

A set is three cards where either the symbols on the cards are all the same or they are all different, the number of symbols on the cards are all the same or all different, the colours are all the same or all different, and the shadings are all the same or all different.

For example, this is a set:

```two solid green ovals
one open green squiggle
three striped green diamonds```

because each card depicts a different symbol, the number of symbols on each card is different, the colours are all the same, and the shadings are all different.

This is not a set:

```two solid purple ovals
one open green squiggle
three striped green diamonds```

because two of the cards are green and one is purple, so the colours are neither all the same nor all different.

• Create a representation of a pack of Set cards, shuffle it, select a specified number of cards from the pack and list them in the output.
• Identify the sets in the selected cards and list them.
Also see

## Factor

```USING: grouping io kernel literals math.combinatorics
prettyprint qw random sequences sequences.product sets ;

CONSTANT: cards \$[
qw{
one two three
solid open striped
red green purple
diamond oval squiggle
} 3 group <product-sequence>
]

: deal ( n -- seq ) cards swap sample ;

: set? ( seq -- ? ) cardinality { 1 3 } member? ;

: sets ( seq -- newseq )
3 [ flip [ set? ] all? ] filter-combinations ;

: .length ( seq str -- ) write bl length . nl ;

: .cards ( seq -- )
[ " " join dup "o" head? "" "s" ? append print ] each nl ;

: .sets ( seq -- )
dup "Sets present:" .length [ .cards ] each ;

: play ( n -- )
deal [ "Cards dealt:" .length ]
[ .cards ]
[ sets .sets ] tri ;

4 8 12 [ play ] tri@
```
Output:
```Cards dealt: 4

two solid purple ovals
three open green diamonds
two striped purple ovals
three solid purple diamonds

Sets present: 0

Cards dealt: 8

two open red squiggles
one open red oval
two striped purple diamonds
one striped green oval
one striped red squiggle
three solid purple ovals
one solid green diamond
three striped purple ovals

Sets present: 1

two open red squiggles
one solid green diamond
three striped purple ovals

Cards dealt: 12

two striped purple diamonds
two open purple ovals
three striped green squiggles
one striped red diamond
three open green diamonds
three open green squiggles
two open green ovals
two solid red diamonds
three open purple squiggles
one open purple squiggle
two solid green ovals
two striped green ovals

Sets present: 2

one striped red diamond
three open purple squiggles
two solid green ovals

two open green ovals
two solid green ovals
two striped green ovals
```

## Julia

```import Base: vec, string, print
import Random: shuffle
import Combinatorics: combinations

const NUMBERS = ["one", "two", "three"]
const SHADINGS = ["solid", "striped", "open"]
const COLORS = ["red", "green", "purple"]
const SYMBOLS = ["diamond", "oval", "squiggle"]

struct SetCard
number::UInt8
color::UInt8
symbol::UInt8
function SetCard(num, sha, col, sym)
@assert all(i -> 1 <= i <= 3, (num, sha, col, sym))
return new(num, sha, col, sym)
end
end

num(s::SetCard) = NUMBERS[s.number]
col(s::SetCard) = COLORS[s.color]
sym(s::SetCard) = SYMBOLS[s.symbol]
Base.vec(sc::SetCard) = [sc.number, sc.shading, sc.color, sc.symbol]
function Base.string(sc::SetCard)
plu = sc.number == 1 ? "" : "s"
return "(" * join([num(sc), sha(sc), col(sc), sym(sc)], " ") * plu * ")"
end
Base.print(io:: IO, sc::SetCard) = print(io, string(sc))
Base.print(io:: IO, vsc::Vector{SetCard}) = print(io, "[" * join(string.(vsc), ", ") * "]")

""" True if the 3 cards form a set according to the Set game rules """
function allsameordifferent(sc1::SetCard, sc2, sc3)
a, b, c = vec(sc1), vec(sc2), vec(sc3)
return all(i -> a[i] == b[i] ==  c[i] || a[i] != b[i] && a[i] != c[i] && b[i] != c[i], eachindex(a))
end

"""  Return a vector of the sets in the vector of SetCards """
function process_deal(cards::Vector{SetCard})
return Iterators.filter(combo -> allsameordifferent(combo...), combinations(cards, 3))
end

function testcardsets()
pack = vec([SetCard(n, sh, c, sy) for n in 1:3, sh in 1:3, c in 1:3, sy in 1:3])
numcards = 81
while !isnothing(numcards)
print("\n\nEnter number of cards to deal (3 to 81, or just a space to exit) => ")
if !isnothing(numcards) && 3 <= numcards <= 81
deal = shuffle(pack)[begin:numcards]
sets = collect(process_deal(deal))
println("\nThe deal is:\n\$deal\n\nThere are \$(length(sets)) sets.")
foreach(println, sets)
end
end
end

testcardsets()
```
Output:
```Enter number of cards to deal (3 to 81, or just a space to exit) => 4

The deal is:
[(one striped red squiggle), (one striped purple diamond), (three solid purple diamonds), (three open red ovals)]

There are 0 sets.

Enter number of cards to deal (3 to 81, or just a space to exit) => 12

The deal is:
[(one striped green squiggle), (one solid green oval), (one open green oval), (one striped red diamond), (one open purple oval), (two open purple squiggles), (one solid red diamond), (three open purple diamonds), (three open green diamonds), (three striped red ovals), (three open green ovals), (two open red ovals)]

There are 3 sets.
[(one striped green squiggle), (one open purple oval), (one solid red diamond)]
[(one open purple oval), (two open purple squiggles), (three open purple diamonds)]
[(one open purple oval), (three open green ovals), (two open red ovals)]

Enter number of cards to deal (3 to 81, or just a space to exit) => 16

The deal is:
[(three open purple squiggles), (one open red diamond), (three striped purple diamonds), (three solid red diamonds), (one solid purple diamond), (one solid green oval), (three solid red ovals), (three solid purple ovals), (one solid green diamond), (two solid green diamonds), (two open purple squiggles), (one open purple squiggle), (three striped purple squiggles), (two solid green squiggles), (three solid red squiggles), (one open purple diamond)]

There are 6 sets.
[(three open purple squiggles), (three striped purple diamonds), (three solid purple ovals)]
[(three open purple squiggles), (two open purple squiggles), (one open purple squiggle)]
[(one open red diamond), (three striped purple diamonds), (two solid green diamonds)]
[(three solid red diamonds), (one solid purple diamond), (two solid green diamonds)]
[(three solid red diamonds), (three solid red ovals), (three solid red squiggles)]
[(one solid purple diamond), (three solid red ovals), (two solid green squiggles)]

Enter number of cards to deal (3 to 81, or just a space to exit) =>
```

## Phix

```with javascript_semantics
constant nums = {"one", "two", "three"},
colours = {"red", "green", "purple"},
symbols = {"diamond", "oval", "squiggle"}

function decode(integer t)
t -= 1
integer n = remainder(t,3)+1,
s = remainder(floor(t/3),3)+1,
c = remainder(floor(t/9),3)+1,
m = remainder(floor(t/27),3)+1
return {n,s,c,m,iff(n=1?"":"s")}
end function

procedure showcard(sequence card)
integer {n,s,c,m} = card
end procedure

procedure showsets(sequence hand)
integer lh = length(hand)
printf(1,"Cards dealt: %d\n%n",{lh,lh!=81})
if lh!=81 then
for c in hand do showcard(decode(c)) end for
end if
sequence sets = {}
for t in combinations(hand,3) do
sequence {c1,c2,c3} = apply(t,decode)
bool found = true
for i=1 to 4 do
if not (c1[i]=c2[i] and c2[i]=c3[i])
and not (c1[i]!=c2[i] and c2[i]!=c3[i] and c1[i]!=c3[i]) then
found = false
exit
end if
end for
if found then
sets = append(sets,{c1,c2,c3})
end if
end for
printf(1,"\nSets present: %d\n\n",length(sets))
if lh!=81 then
for s in sets do
for c in s do showcard(c) end for
printf(1,"\n")
end for
end if
end procedure

sequence pack = tagset(81)
for deal in {4,8,12,81} do
pack = shuffle(pack)
showsets(pack[1..deal])
end for
```
Output:
```Cards dealt: 4

three open purple ovals
two solid green ovals
three solid red squiggles
three striped purple diamonds

Sets present: 0

Cards dealt: 8

two striped purple squiggles
three striped red squiggles
one striped green squiggle
two open purple diamonds
three solid green squiggles
two solid green squiggles
one striped purple oval
two solid purple squiggles

Sets present: 1

three striped red squiggles
one striped green squiggle
two striped purple squiggles

Cards dealt: 12

two open green diamonds
two striped purple diamonds
two open purple ovals
two solid red ovals
three solid purple squiggles
three striped green ovals
three solid green diamonds
one striped purple diamond
three solid green ovals
one open purple oval
three solid red diamonds
three solid purple ovals

Sets present: 5

three solid red diamonds
two open green diamonds
one striped purple diamond

three solid red diamonds
three solid green ovals
three solid purple squiggles

one striped purple diamond
two open purple ovals
three solid purple squiggles

two striped purple diamonds
one open purple oval
three solid purple squiggles

two solid red ovals
three striped green ovals
one open purple oval

Cards dealt: 81

Sets present: 1080
```

## Python

```from itertools import combinations
from itertools import product
from random import shuffle
from typing import Iterable
from typing import List
from typing import NamedTuple
from typing import Tuple

NUMBERS = ("one", "two", "three")
SHAPES = ("diamond", "squiggle", "oval")
COLORS = ("red", "green", "purple")

class Card(NamedTuple):
number: str
color: str
shape: str

def __str__(self) -> str:
s = " ".join(self)
if self.number != "one":
s += "s"
return s

Cards = List[Card]

def new_deck() -> Cards:
"""Return a new shuffled deck of 81 unique cards."""
deck = [Card(*features) for features in product(NUMBERS, SHADING, COLORS, SHAPES)]
shuffle(deck)
return deck

def deal(deck: Cards, n: int) -> Tuple[Cards, Cards]:
"""Return _n_ cards from the top of the deck and what remains of the deck."""
return deck[:n], deck[n:]

def is_set(cards: Tuple[Card, Card, Card]) -> bool:
"""Return _True_ if _cards_ forms a set."""
return (
same_or_different(c.number for c in cards)
and same_or_different(c.shape for c in cards)
and same_or_different(c.shading for c in cards)
and same_or_different(c.color for c in cards)
)

def same_or_different(features: Iterable[str]) -> bool:
"""Return _True_ if _features_ are all the same or all different."""
return len(set(features)) in (1, 3)

def print_sets_from_new_deck(n: int) -> None:
"""Display sets found in _n_ cards dealt from a new shuffled deck."""
table, _ = deal(new_deck(), n)
print(f"Cards dealt: {n}\n")
print("\n".join(str(card) for card in table), end="\n\n")

sets = [comb for comb in combinations(table, 3) if is_set(comb)]
print(f"Sets present: {len(sets)}\n")
for _set in sets:
print("\n".join(str(card) for card in _set), end="\n\n")

print("----")

if __name__ == "__main__":
for n in (4, 8, 12):
print_sets_from_new_deck(n)
```
Output:
```Cards dealt: 4

two open green diamonds
three striped green ovals
two open purple ovals
two open red squiggles

Sets present: 1

two open green diamonds
two open purple ovals
two open red squiggles

----
Cards dealt: 8

three striped purple diamonds
one solid purple oval
two open purple diamonds
three solid purple diamonds
one solid green squiggle
three open green squiggles
three open purple squiggles
three solid purple ovals

Sets present: 1

three striped purple diamonds
three open purple squiggles
three solid purple ovals

----
Cards dealt: 12

two open green squiggles
three solid purple ovals
three open red diamonds
two open red squiggles
three open purple ovals
three open red squiggles
three striped red squiggles
two open purple diamonds
three solid red squiggles
one solid red squiggle
two striped purple diamonds
one solid red diamond

Sets present: 2

two open red squiggles
three striped red squiggles
one solid red squiggle

three open red squiggles
three striped red squiggles
three solid red squiggles

----
```

## Quackery

Why does `isset`, the word that tests if three cards constitute a set, use `+` and `mod`?

If we map any of the properties, say colour, onto the numbers 0, 1 and 2, then the sum of three colours mod 3 is 0 if and only if all the colours are different or all the colours are the same. This can be confirmed exhaustively, or for the underlying mathematics see the first two paragraphs of the section "A Mathematical Perspective" (pages 7 and 8) in this paper:

SETs and Anti-SETs: The Math Behind the Game of SET, by Charlotte Chan

`transpose` is defined at Matrix transposition#Quackery.

`comb` and `arrange` are defined at Combinations#Quackery.

```  [ true swap transpose witheach
[ 0 swap witheach +
3 mod if [ not conclude ] ] ]         is isset    ( [ --> b )

[ [ [] 81 times
[ i 4 times [ 3 /mod swap ]
drop 3 times join
nested join ] ] constant
shuffle swap split drop ]                 is cards    ( n --> [ )

[ [] swap dup size swap 3 rot comb
witheach
[ dip dup arrange
dup isset iff
[ nested rot join swap ]
else drop ] drop ]                    is sets     ( [ --> [ )

[ unpack dup dip
[ [ table
\$ "one" \$ "two" \$ "three" ]
do echo\$ sp
[ table
\$ "solid" \$ "striped" \$ "open" ]
do echo\$ sp
[ table
\$ "red" \$ "green" \$ "purple" ]
do echo\$ sp
[ table
\$ "diamond" \$ "squiggle" \$ "oval" ]
do echo\$ ]
if [ say "s" ] cr ]                       is echocard ( [ -->   )

[ dup cards swap
cr say "Cards dealt: " echo cr cr
dup witheach echocard cr
sets dup size
say "Sets present: " echo cr cr
witheach [ witheach echocard cr ] ]       is play     ( n -->   )

' [ 4 8 12 ] witheach [ play say "-----" ]```
Output:
```Cards dealt: 4

two striped green squiggles
one open purple oval
one solid purple diamond
three open red diamonds

Sets present: 0

-----
Cards dealt: 8

three open purple squiggles
two open purple ovals
three solid purple ovals
three solid red squiggles
two striped purple diamonds
two solid green squiggles
one striped green oval
one open purple diamond

Sets present: 1

three open purple squiggles
two open purple ovals
one open purple diamond

-----
Cards dealt: 12

one solid green diamond
one striped red diamond
one open purple squiggle
two solid green diamonds
two striped green squiggles
two solid red ovals
two solid green squiggles
one open green squiggle
two solid green ovals
two solid red diamonds
one open purple diamond
three striped purple diamonds

Sets present: 3

two solid red ovals
one open green squiggle
three striped purple diamonds

two solid green diamonds
two solid green squiggles
two solid green ovals

one solid green diamond
one striped red diamond
one open purple diamond

-----```

## Wren

Library: Wren-ioutil
Library: Wren-fmt
Library: Wren-perm

Note that entering 81 for the number of cards to deal confirms that there are 1080 possible sets.

```import "random" for Random
import "./ioutil" for Input
import "./fmt" for Fmt
import "./perm" for Comb

var nums = ["one", "two", "three"]
var shas = ["solid", "striped", "open"]
var cols = ["red", "green", "purple"]
var syms = ["diamond", "oval", "squiggle"]

var pack = List.filled(81, null)
var i = 0
for (num in 0..2) {
for (sha in 0..2) {
for (col in 0..2) {
for (sym in 0..2) {
pack[i] = [nums[num], shas[sha], cols[col], syms[sym]]
i = i + 1
}
}
}
}

var printCards = Fn.new { |cards|
for (card in cards) {
var pl = card[0] != "one" ? "s" : ""
Fmt.print("\$s \$s \$s \$s\$s", card[0], card[1], card[2], card[3], pl)
}
}

var findSets = Fn.new { |cards|
var sets = []
var trios = Comb.list(cards, 3)
for (trio in trios) {
var t1 = trio[0]
var t2 = trio[1]
var t3 = trio[2]
var found = true
for (i in 0..3) {
if (t1[i] == t2[i] && t2[i] == t3[i]) continue
if (t1[i] != t2[i] && t2[i] != t3[i] && t1[i] != t3[i]) continue
found = false
break
}
}
Fmt.print("Sets present: \$d\n", sets.count)
if (sets.count > 0) {
for (set in sets) {
printCards.call(set)
System.print()
}
}
}

var prompt = "Enter number of cards to deal - 3 to 81 or q to quit: "
Input.quit = "q"
while(true) {
Random.new().shuffle(pack) // shuffle for each deal
var i = Input.integer(prompt, 3, 81)
if (i == Input.quit) return
var dealt = pack[0...i]
System.print()
printCards.call(dealt)
System.print()
findSets.call(dealt)
}
```
Output:

Sample run:

```Enter number of cards to deal - 3 to 81 or q to quit: 4

three solid green diamonds
one solid red diamond
one solid green oval
three striped purple squiggles

Sets present: 0

Enter number of cards to deal - 3 to 81 or q to quit: 8

one open green squiggle
one open purple squiggle
one solid green squiggle
three solid purple squiggles
three open green squiggles
one striped red diamond
one striped green oval
one striped green squiggle

Sets present: 1

one open green squiggle
one solid green squiggle
one striped green squiggle

Enter number of cards to deal - 3 to 81 or q to quit: 12

three open green ovals
three striped green diamonds
one solid purple oval
one striped purple diamond
two open green diamonds
three solid red diamonds
three solid red ovals
three solid green diamonds
three striped red ovals
three striped red squiggles
two open red squiggles
one solid green oval

Sets present: 3

three striped green diamonds
one solid purple oval
two open red squiggles

one solid purple oval
two open green diamonds
three striped red squiggles

one striped purple diamond
two open green diamonds
three solid red diamonds

Enter number of cards to deal - 3 to 81 or q to exit: q
```