Perfect Shuffle Challenge

[lrobbo314]

I was looking at this old challenge from @MrExcel, 'Perfect Shuffle Challenge'. It's from back in 2013. I thought that it would be fun to try this challenge with the new dynamic array formulas.

The objective is to see how many times you would need to do a perfect riffle shuffle in order for the deck to get back in its original order. I used 2 formulas. SHUFFLE, and RX, which is a recursive function.

SHUFFLE

=LAMBDA(deck,LET(d,deck,r,ROWS(d),s,SEQUENCE(r,,0),cc,HSTACK(TAKE(d,r/2),TAKE(d,-r/2)),INDEX(cc,QUOTIENT(s,2)+1,MOD(s,2)+1)))

RX

=LAMBDA(rng,[cnt],LET(s,SHUFFLE(rng),IF(AND(s=SEQUENCE(ROWS(s))),cnt+1,RX(s,cnt+1))))

PERFECT SHUFFLE
	H	I
2	4	2
3	6	4
4	8	3
5	10	6
6	12	10
7	14	12
8	16	4
9	18	8
10	20	18
11	22	6
12	24	11
13	26	20
14	28	18
15	30	28
16	32	5
17	34	10
18	36	12
19	38	36
20	40	12
21	42	20
22	44	14
23	46	12
24	48	23
25	50	21
26	52	8
27	54	52
28	56	20
29	58	18
30	60	58
31	62	60
32	64	6
33	66	12
34	68	66
35	70	22
Sheet1

Cell Formulas
Range	Formula
H2:H301	H2	=SEQUENCE(300,,4,2)
I2:I35	I2	=RX(SEQUENCE(H2))
Dynamic array formulas.

 

[lrobbo314]

Just playing around with this some more. Changing how the cards are shuffled together, i.e. which deck you use first after splitting the whole deck, means that it will take 52 shuffles to re-order the deck as opposed to only 8. I was only able to post half of the shuffles because of the character limit on the posts. I used unichar symbols to show the cards and a little conditional formatting to get the red and black decks.

Also, the shuffle formula is completely different using SEQUENCE, TOCOL, and CHOOSECOLS instead of MOD and QUOTIENT.

SHUFFLE
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z	AA	AB
1	New Deck		1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
2	🂡		🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾
3	🂢		🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽
4	🂣		🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻
5	🂤		🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺
6	🂥		🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹
7	🂦		🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸
8	🂧		🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷
9	🂨		🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶
10	🂩		🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵
11	🂪		🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴
12	🂫		🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳
13	🂭		🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲
14	🂮		🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱
15	🃁		🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞
16	🃂		🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝
17	🃃		🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛
18	🃄		🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚
19	🃅		🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙
20	🃆		🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘
21	🃇		🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗
22	🃈		🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖
23	🃉		🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕
24	🃊		🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔
25	🃋		🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓
26	🃍		🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒
27	🃎		🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑
28	🃑		🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎
29	🃒		🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍
30	🃓		🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋
31	🃔		🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊
32	🃕		🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉
33	🃖		🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈
34	🃗		🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇
35	🃘		🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆
36	🃙		🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅
37	🃚		🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄
38	🃛		🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃
39	🃝		🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂
40	🃞		🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁
41	🂱		🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮
42	🂲		🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭
43	🂳		🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫
44	🂴		🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪
45	🂵		🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥	🃓	🂲	🂸	🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩
46	🂶		🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨
47	🂷		🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧
48	🂸		🂻	🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦
49	🂹		🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡	🃑	🂱	🃇	🂪	🂥
50	🂺		🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤
51	🂻		🃍	🃞	🂷	🃊	🃝	🃆	🃚	🃅	🂩	🃕	🂳	🃈	🃛	🂶	🂺	🂽	🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣
52	🂽		🂾	🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢
53	🂾		🃎	🂮	🃗	🂴	🂹	🃋	🂭	🂦	🂣	🃒	🃁	🂧	🃔	🃂	🃘	🃄	🃙	🂵	🃉	🂫	🃖	🃃	🂨	🂤	🂢	🂡
Sheet1

Cell Formulas
Range	Formula
C1:BB1	C1	=SEQUENCE(,52)
A2:A53	A2	=DECK()
C2:C53	C2	=SHUFFLE(A2#)
D2:AB53	D2	=SHUFFLE(C2#)
Dynamic array formulas.

NRNG

=LAMBDA(start,end,skip,LET(s,SEQUENCE(end-start+1,,start),UNICHAR(FILTER(s,s<>skip))))

DECK

=LAMBDA(LET(spades,NRNG(127137,127150,127148),hearts,NRNG(127153,127166,127164),diamonds,NRNG(127169,127182,127180),clubs,NRNG(127185,127198,127196),VSTACK(spades,diamonds,clubs,hearts)))

SHUFFLE

=LAMBDA(deck,INDEX(deck,TOCOL(CHOOSECOLS(TRANSPOSE(SEQUENCE(2,ROWS(deck)/2)),2,1))))