WR

[Xlambda]

WR: Word maze Results challenge. Please do see latest (26-Oct-21) YT video of MrExcel Solving Word Search With Excel (FMWC) - 2439
This is a compact set of functions that can solve all lookup scenarios.
Defined names: ar, sample array ( A1:T15 ) ; rw, nr. rows of sample array (15) (width is fixed to 20) ; cs, constant array values for "snake" lookup {-1,1, 20,-20} ; cd, constant array values for "diagonal" lookup {-21,-19,19,21}

WL(l)=LAMBDA(l,LET(x,IF(ar=l,1),y,IF(ar="?",1),z,IF(x+y,1),v,IF(z,SEQUENCE(rw,20)),SMALL(v,SEQUENCE(COUNT(v)))))
WA(a,c)=LAMBDA(a,c,LET(x,a-c,y,IF(x>0,x),UNIQUE(SMALL(y,SEQUENCE(COUNT(y ))))))
WB(a,b)=LAMBDA(a,b,FILTER(a,IFNA(XMATCH(a,b,,2),0)))
WR(w,c,[r],[i ])=LAMBDA(w,c,[r],[i ],LET(n,IF(i,i,LEN(w)),x,MID(w,n,1),y,MID(w,n-1,1),z,IF(AND(r=0),WA(WL(x),c),WA(r,c)),IF(n=1,r,WR(w,c,WB(z,WL(y )),n-1))))
Last one WR is !! recursive !! Define the names, then the functions and we are good to go. (Gaps in [i ] are to keep the text no to turn italics)
Will come back with the "concept" explanation asap.

=LAMBDA(w,c,[r],[i ],LET(n,IF(i,i,LEN(w)),x,MID(w,n,1),y,MID(w,n-1,1),z,
     IF(AND(r=0),WA(WL(x),c),WA(r,c)),IF(n=1,r,WR(w,c,WB(z,WL(y)),n-1))
    )
)

WORD MAZE.xlsx
	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	AC	AD	AE	AF	AG	AH	AI	AJ	AK
1	Z	1	S	G	P	E	2	T	H	E	D	I	Z	B	A	N	T	S	N	S			defined names
2	S	P	?	A	K	I	W	K	1	F	H	V	Z	G	2	I	E	K	A	X			ar: A1:T15 (sample array)
3	?	I	T	Q	E	?	L	A	S	I	X	Q	J	N	S	X	4	T	J	K			rw: 15 (width is always 20)
4	L	E	N	J	F	X	A	4	T	I	K	N	S	B	X	1	D	J	C	P			cs: {-1,1,20,-20} (constant array for "snake" type lookup
5	G	D	L	3	3	D	M	V	L	T	G	K	?	C	U	3	O	Q	O	O			cd: {-21,-19,19,21} (constant array for "diagonal" type lookup
6	I	A	I	U	V	G	Y	L	U	?	I	E	P	3	W	G	K	B	T	P
7	4	A	P	A	U	4	C	Z	V	F	F	F	A	F	I	P	A	X	T	T			"snake" lookup						"diagonal" lookup
8	H	N	?	4	G	C	K	S	4	I	D	R	H	N	N	A	J	D	N	S
9	E	C	3	X	C	O	D	B	V	Q	O	Y	J	E	R	G	S	K	A	H			=WR("snake",cs)						=WR("diagonal",cd)
10	E	X	1	Z	?	P	N	I	3	O	W	C	C	N	2	U	R	E	G	J			3						82
11	E	O	N	M	E	V	K	A	B	E	P	F	L	Q	N	Z	?	E	W	3			18
12	K	A	N	?	A	I	B	K	L	G	2	4	?	N	?	Z	B	N	Q	E			20						=WR("advance",cd)
13	S	M	O	4	Y	F	B	B	R	E	?	D	N	E	1	A	D	J	M	4			160						67
14	C	F	X	4	3	T	Y	1	Z	J	N	I	W	U	Z	3	O	W	H	M			224
15	T	Y	D	2	Y	Z	S	U	D	V	V	F	4	O	Z	E	K	A	?	S			300
16
17	=SEQUENCE(rw,20)																						=WR("difficult",cs)
18	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20			151
19	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40
20	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60			=WR("winner",cs)
21	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80			115
22	81	82	83	84	85	86	87	88	89	90	91	92	93	94	95	96	97	98	99	100			273
23	101	102	103	104	105	106	107	108	109	110	111	112	113	114	115	116	117	118	119	120
24	121	122	123	124	125	126	127	128	129	130	131	132	133	134	135	136	137	138	139	140
25	141	142	143	144	145	146	147	148	149	150	151	152	153	154	155	156	157	158	159	160		Note: I left the results in "sequence numbers" representation on purpose,
26	161	162	163	164	165	166	167	168	169	170	171	172	173	174	175	176	177	178	179	180		to be much easier to visualize the results.
27	181	182	183	184	185	186	187	188	189	190	191	192	193	194	195	196	197	198	199	200		To get them to "range" representation we can use PR(a) (print results)
28	201	202	203	204	205	206	207	208	209	210	211	212	213	214	215	216	217	218	219	220		PR(a)=LAMBDA(a,LET(x,QUOTIENT(a-1,20)+1,y,MOD(a-1,20)+1,ADDRESS(x,y,4)))
29	221	222	223	224	225	226	227	228	229	230	231	232	233	234	235	236	237	238	239	240
30	241	242	243	244	245	246	247	248	249	250	251	252	253	254	255	256	257	258	259	260
31	261	262	263	264	265	266	267	268	269	270	271	272	273	274	275	276	277	278	279	280			C1						B5
32	281	282	283	284	285	286	287	288	289	290	291	292	293	294	295	296	297	298	299	300			R1
33																							T1						G4
34	Important Note: Covered here only snake and diagonal search, for being the more complicated ones.																						T8
35	Anyhow, to cover the rest of them the only thing we have to do is defining new constant arrays																						D12
36	cs (constant snake) {-1,1,20,-20}																						T15
37	cd (constant diagonal) {-21,-19,19,21}
38	For example, for horizontal lookup we have to define																						K8
39	ch {-1,1} and for vertical cv: {-20,20}
40																							O6
41																							M14
42
43
WM snake diagonal

Cell Formulas
Range	Formula
W9,W20,W17,A17,AC12,AC9	W9	=FORMULATEXT(W10)
W10:W15	W10	=WR("snake",cs)
AC10	AC10	=WR("diagonal",cd)
AC13	AC13	=WR("advance",cd)
A18:T32	A18	=SEQUENCE(rw,20)
W18	W18	=WR("difficult",cs)
W21:W22	W21	=WR("winner",cs)
W31:W36	W31	=PR(W10#)
AC31	AC31	=PR(AC10)
AC33,W38	AC33	=PR(AC13)
W40:W41	W40	=PR(W21#)
Dynamic array formulas.

Named Ranges
Name	Refers To	Cells
ar	='WM snake diagonal'!$A$1:$T$15	AC13, AC10, W21, W18, W10

 

[Xlambda]

Few examples before revealing the concept.

Play Free Sudoku online - solve web sudoku puzzles

Play free Sudoku online from Easy to Expert level on Sudoku.com. Select a difficulty level of a web sudoku puzzle to challenge yourself and enjoy the game!

sudoku.com

SDK array.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X
1		extreme sudokus from sudoku.com
2												=SK.2IJ(B3:J11)
3					7	5						5 218	2	8	4	7	5	3	1	9	6
4					2		8		4	5			3	9	6	2	1	8	7	4	5
5			5							2			1	5	7	4	9	6	8	3	2
6			7				1						6	7	2	5	3	1	9	8	4
7		8		1		4	9	2		7			8	3	1	6	4	9	2	5	7
8				9		2		6					5	4	9	8	2	7	6	1	3
9		4	1							8			4	1	5	9	6	2	3	7	8
10				3				4					7	6	3	1	8	5	4	2	9
11				8			4	5	6				9	2	8	3	7	4	5	6	1
12
13												SK.2IJ function solves using recursion and also shows info about recursive loops.
14												2nd value, total loops, 1st value, nr. of iterations of last loop that solved the puzzle.
15
Sheet3

Cell Formulas
Range	Formula
L2	L2	=FORMULATEXT(L3)
L3:U11	L3	=SK.2IJ(B3:J11)
Dynamic array formulas.

SDK array.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V
15
16												=SK.2IJ(B17:J25)
17				7		1			6	5		4 76	4	2	7	3	1	9	8	6	5
18		9			7			2					9	1	5	7	8	6	2	4	3
19			8										6	8	3	4	5	2	7	9	1
20			9				1			7			5	9	8	2	6	1	4	3	7
21				4				9	1				7	6	4	8	3	5	9	1	2
22			3										1	3	2	9	7	4	5	8	6
23				1		4			2	9			8	7	1	5	4	3	6	2	9
24						2			5				3	4	9	6	2	7	1	5	8
25			5					3					2	5	6	1	9	8	3	7	4
26
Sheet3

Cell Formulas
Range	Formula
L16	L16	=FORMULATEXT(L17)
L17:U25	L17	=SK.2IJ(B17:J25)
Dynamic array formulas.

SDK array.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V
26
27												how many loops for "creating" a solved puzzle from scratch
28												=SK.2IJ(B29:J37)
29												29 403	6	5	3	8	4	9	7	1	2
30													8	9	1	3	2	7	6	4	5
31													2	7	4	1	6	5	3	8	9
32													4	2	8	7	3	6	9	5	1
33													1	6	5	2	9	8	4	7	3
34													9	3	7	5	1	4	2	6	8
35													3	4	9	6	5	1	8	2	7
36													7	1	2	4	8	3	5	9	6
37													5	8	6	9	7	2	1	3	4
38
Sheet3

Cell Formulas
Range	Formula
L28	L28	=FORMULATEXT(L29)
L29:U37	L29	=SK.2IJ(B29:J37)
Dynamic array formulas.

 

[Xlambda]

A simpler solution, for a single function, but this time with 5x5 of 9x9 arrays on which every row and every column of any next 9x9 array has no dups (SUDOKUs have also every next 3x3 arrays with no dups)
It's iterative, 5 in 5 loops of 3M iterations => total 75M iterations
NK(n,k) delivers kxk of nxn arrays Each nxn array has no dups byrow or bycol

=LAMBDA(n, k,
    LET(
        s, SEQUENCE(n),
        q, SEQUENCE(k),
        r, LAMBDA(n, TOROW(SORTBY(s, RANDARRAY(n)))),
        c, LAMBDA(x, AND(BYCOL(x, LAMBDA(y, ROWS(UNIQUE(y)) = ROWS(x))))),
        b, LAMBDA(x,
            REDUCE(
                r(n),
                SEQUENCE(10 ^ 6, 3),
                LAMBDA(v, i, IF(ROWS(v) = x, v, LET(a, VSTACK(v, r(x)), IF(c(a), a, v))))
            )
        ),
        DROP(REDUCE("", q, LAMBDA(v, i, VSTACK(v, DROP(REDUCE("", q, LAMBDA(v, i, HSTACK(v, b(n)))), , 1)))), 1)
    )
)

NNK.xlsx
	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	AC	AD	AE	AF	AG	AH	AI	AJ	AK	AL	AM	AN	AO	AP	AQ	AR	AS	AT	AU
1
2		=NK(9,5)
3		6	1	8	3	4	5	9	7	2	1	7	9	8	6	3	4	2	5	3	1	2	9	5	4	6	7	8	6	7	2	5	1	8	3	9	4	3	4	6	9	2	5	7	1	8
4		9	2	6	8	5	1	7	4	3	7	9	5	1	4	8	6	3	2	5	4	9	3	7	8	1	2	6	5	6	1	2	7	3	8	4	9	7	5	2	8	4	9	3	6	1
5		4	3	5	7	8	9	6	2	1	5	8	6	4	2	7	3	9	1	7	3	4	8	2	6	9	5	1	7	3	5	6	9	1	4	8	2	1	6	8	5	9	3	2	4	7
6		3	6	1	4	7	8	2	5	9	6	2	7	5	1	9	8	4	3	2	6	7	5	1	9	3	8	4	1	8	9	3	4	6	2	7	5	2	8	9	1	6	7	4	5	3
7		7	5	4	1	9	2	3	6	8	2	3	4	7	9	5	1	8	6	1	2	3	4	9	7	8	6	5	9	2	4	8	3	5	1	6	7	5	1	4	7	8	2	6	3	9
8		2	8	3	9	6	4	5	1	7	9	5	3	6	7	4	2	1	8	4	9	6	7	8	5	2	1	3	3	5	8	4	6	9	7	2	1	6	9	3	2	7	4	1	8	5
9		1	7	9	5	2	3	4	8	6	3	4	1	2	8	6	9	5	7	8	7	5	6	3	1	4	9	2	2	9	6	7	8	4	5	1	3	9	3	7	4	5	1	8	2	6
10		8	4	7	2	3	6	1	9	5	4	1	8	3	5	2	7	6	9	9	8	1	2	6	3	5	4	7	8	4	3	1	2	7	9	5	6	8	2	5	3	1	6	9	7	4
11		5	9	2	6	1	7	8	3	4	8	6	2	9	3	1	5	7	4	6	5	8	1	4	2	7	3	9	4	1	7	9	5	2	6	3	8	4	7	1	6	3	8	5	9	2
12		5	3	9	7	2	4	8	1	6	4	6	2	7	9	3	8	1	5	7	8	6	5	3	4	1	2	9	4	9	5	8	2	1	7	3	6	8	5	7	9	6	1	4	2	3
13		2	1	7	8	3	5	6	4	9	2	1	3	9	5	6	7	8	4	6	5	4	1	9	2	3	8	7	5	2	8	7	6	4	3	1	9	9	3	4	1	5	6	2	7	8
14		7	5	6	1	4	8	9	2	3	6	5	8	1	4	2	9	3	7	1	9	5	8	2	7	4	3	6	2	7	1	5	4	3	6	9	8	5	1	8	2	9	4	6	3	7
15		9	7	1	6	5	3	2	8	4	5	7	4	3	6	8	1	2	9	4	2	7	9	1	5	8	6	3	7	3	6	9	8	2	4	5	1	1	7	9	8	2	3	5	6	4
16		3	9	5	2	8	7	4	6	1	3	8	9	5	1	7	2	4	6	8	3	1	7	5	9	6	4	2	9	5	3	4	1	7	8	6	2	6	2	1	4	3	7	9	8	5
17		8	6	4	3	7	9	1	5	2	1	2	5	6	7	4	3	9	8	9	7	2	3	4	6	5	1	8	6	4	9	2	5	8	1	7	3	3	8	6	7	4	9	1	5	2
18		6	2	8	4	9	1	3	7	5	7	4	1	2	8	9	6	5	3	3	6	8	2	7	1	9	5	4	1	8	2	6	3	5	9	4	7	7	4	2	5	1	8	3	9	6
19		1	4	3	5	6	2	7	9	8	8	9	7	4	3	1	5	6	2	5	4	9	6	8	3	2	7	1	3	6	4	1	7	9	2	8	5	4	6	5	3	7	2	8	1	9
20		4	8	2	9	1	6	5	3	7	9	3	6	8	2	5	4	7	1	2	1	3	4	6	8	7	9	5	8	1	7	3	9	6	5	2	4	2	9	3	6	8	5	7	4	1
21		8	5	7	1	6	3	9	2	4	6	9	7	3	1	4	5	8	2	3	7	1	2	9	4	8	6	5	9	4	5	2	3	8	1	6	7	7	3	5	8	9	1	2	4	6
22		9	3	2	8	4	6	1	5	7	3	4	8	7	9	6	1	2	5	1	8	2	6	7	5	9	3	4	7	6	4	9	1	5	3	2	8	1	7	6	5	3	4	9	2	8
23		2	6	9	7	1	5	4	8	3	2	5	4	8	6	7	9	1	3	2	1	9	4	5	7	3	8	6	5	7	1	6	2	4	9	8	3	6	1	2	9	7	3	4	8	5
24		6	2	4	3	5	9	7	1	8	9	2	1	6	8	5	3	7	4	9	2	4	1	8	6	5	7	3	1	8	3	4	9	6	2	7	5	3	9	8	4	6	2	7	5	1
25		7	9	5	4	3	2	8	6	1	1	7	3	2	4	9	8	5	6	8	9	7	3	6	2	4	5	1	6	2	9	8	4	3	7	5	1	9	6	1	2	4	8	5	3	7
26		1	7	8	2	9	4	6	3	5	8	6	9	1	5	3	2	4	7	7	3	8	5	2	1	6	4	9	4	3	2	7	8	1	5	9	6	2	8	9	7	5	6	3	1	4
27		5	8	1	9	2	7	3	4	6	7	8	2	5	3	1	4	6	9	6	4	5	7	3	8	1	9	2	8	1	7	5	6	9	4	3	2	4	5	3	6	1	7	8	9	2
28		3	4	6	5	8	1	2	7	9	4	1	5	9	7	2	6	3	8	4	5	6	9	1	3	7	2	8	2	9	8	3	5	7	6	1	4	5	2	4	1	8	9	6	7	3
29		4	1	3	6	7	8	5	9	2	5	3	6	4	2	8	7	9	1	5	6	3	8	4	9	2	1	7	3	5	6	1	7	2	8	4	9	8	4	7	3	2	5	1	6	9
30		5	9	2	4	3	6	7	1	8	2	1	4	9	5	8	7	6	3	3	7	4	2	1	5	6	8	9	5	4	6	1	2	8	3	7	9	8	5	6	1	9	2	3	4	7
31		1	3	5	6	4	8	2	7	9	3	9	5	4	8	2	1	7	6	7	3	1	5	9	6	2	4	8	7	2	5	6	8	1	9	3	4	3	9	4	5	8	6	7	2	1
32		6	4	7	9	2	1	8	5	3	8	7	6	5	2	1	3	4	9	5	6	3	1	2	8	9	7	4	3	5	2	7	1	9	8	4	6	6	2	1	4	7	9	5	3	8
33		8	7	6	1	5	9	3	2	4	4	5	3	8	6	9	2	1	7	2	9	7	6	8	4	3	5	1	8	6	1	2	9	4	7	5	3	4	3	5	6	1	8	9	7	2
34		2	1	3	5	8	4	6	9	7	7	8	2	6	1	3	5	9	4	9	4	2	8	6	3	5	1	7	4	7	9	8	3	2	5	6	1	2	8	3	7	5	4	6	1	9
35		7	2	9	8	6	3	1	4	5	5	3	7	2	9	4	6	8	1	1	5	8	3	4	2	7	9	6	2	1	7	4	5	3	6	9	8	5	6	7	9	4	1	2	8	3
36		3	5	4	2	1	7	9	8	6	1	4	8	7	3	6	9	2	5	8	1	5	9	3	7	4	6	2	6	8	3	9	4	7	1	2	5	1	7	8	3	2	5	4	9	6
37		9	8	1	3	7	5	4	6	2	6	2	9	1	7	5	4	3	8	4	8	6	7	5	9	1	2	3	1	9	4	3	6	5	2	8	7	7	1	9	2	6	3	8	5	4
38		4	6	8	7	9	2	5	3	1	9	6	1	3	4	7	8	5	2	6	2	9	4	7	1	8	3	5	9	3	8	5	7	6	4	1	2	9	4	2	8	3	7	1	6	5
39		1	5	9	4	7	2	3	8	6	5	3	2	8	6	9	4	7	1	6	4	7	8	1	2	5	9	3	2	8	6	7	4	5	9	3	1	3	4	7	8	6	5	2	9	1
40		6	1	2	3	4	5	7	9	8	9	2	8	5	1	4	7	3	6	1	8	3	2	9	5	4	6	7	3	7	2	4	6	9	5	1	8	5	1	3	6	8	9	7	2	4
41		2	6	5	7	8	1	9	4	3	4	1	6	2	9	7	3	8	5	4	3	9	5	6	8	2	7	1	9	2	4	5	1	8	6	7	3	7	8	9	5	4	3	6	1	2
42		3	7	1	8	2	4	6	5	9	3	7	9	6	2	8	1	5	4	5	2	8	9	7	1	3	4	6	1	5	3	2	7	4	8	9	6	8	7	4	3	1	2	9	5	6
43		8	9	6	2	5	3	1	7	4	1	6	5	9	7	3	2	4	8	8	9	2	1	3	7	6	5	4	7	4	5	1	8	6	3	2	9	4	6	2	1	5	7	3	8	9
44		7	4	8	1	9	6	2	3	5	8	5	3	7	4	1	6	9	2	7	6	1	4	5	3	9	8	2	4	1	9	6	5	3	2	8	7	2	3	1	4	9	6	5	7	8
45		5	2	3	9	1	8	4	6	7	7	9	4	1	5	6	8	2	3	2	1	4	6	8	9	7	3	5	6	3	8	9	2	7	1	5	4	9	5	8	2	7	1	4	6	3
46		4	3	7	5	6	9	8	1	2	2	4	1	3	8	5	9	6	7	3	5	6	7	2	4	8	1	9	5	9	7	8	3	1	4	6	2	6	2	5	9	3	8	1	4	7
47		9	8	4	6	3	7	5	2	1	6	8	7	4	3	2	5	1	9	9	7	5	3	4	6	1	2	8	8	6	1	3	9	2	7	4	5	1	9	6	7	2	4	8	3	5
48
Sheet2

Cell Formulas
Range	Formula
B2	B2	=FORMULATEXT(B3)
B3:AT47	B3	=NK(9,5)
Dynamic array formulas.

A lambda that has number of iterations "ni" as separate parameter
(I found the solution with real SUDOKU's far more challenging, this is only if someone prefers a sigle cell formula)
NK(n,k,ni) delivers kxk of nxn arrays using a "k" in "k" loops of "ni"x3 iterations for each loop => k*k*ni*3 iterations. (ni grows "mega" exponential with the size of "n" (for n=5, ni=1000 is enough)

=LAMBDA(n, k, ni,
    LET(
        s, SEQUENCE(n),
        q, SEQUENCE(k),
        r, LAMBDA(n, TOROW(SORTBY(s, RANDARRAY(n)))),
        c, LAMBDA(x, AND(BYCOL(x, LAMBDA(y, ROWS(UNIQUE(y)) = ROWS(x))))),
        b, LAMBDA(x,
            REDUCE(
                r(n),
                SEQUENCE(ni, 3),
                LAMBDA(v, i, IF(ROWS(v) = x, v, LET(a, VSTACK(v, r(x)), IF(c(a), a, v))))
            )
        ),
        DROP(
            REDUCE(
                "",
                q,
                LAMBDA(v, i, VSTACK(v, DROP(REDUCE("", q, LAMBDA(v, i, HSTACK(v, b(n)))), , 1)))
            ),
            1
        )
    )
)

Book1
	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
1
2		=NK(4,3,100)
3		3	4	1	2	4	1	3	2	4	3	2	1
4		2	1	3	4	2	4	1	3	3	4	1	2
5		1	2	4	3	1	3	2	4	1	2	3	4
6		4	3	2	1	3	2	4	1	2	1	4	3
7		4	3	2	1	1	2	3	4	2	3	1	4
8		3	4	1	2	4	1	2	3	1	4	2	3
9		1	2	3	4	2	3	4	1	4	1	3	2
10		2	1	4	3	3	4	1	2	3	2	4	1
11		1	3	2	4	1	4	2	3	2	4	3	1
12		3	2	4	1	4	2	3	1	3	1	2	4
13		4	1	3	2	2	3	1	4	4	3	1	2
14		2	4	1	3	3	1	4	2	1	2	4	3
15
16		=NK(5,5,1000)
17		4	2	3	1	5	5	2	3	4	1	3	2	4	1	5	5	2	3	1	4	2	4	3	5	1
18		2	3	1	5	4	2	3	4	1	5	2	3	1	5	4	1	3	2	4	5	5	1	2	4	3
19		5	1	2	4	3	3	1	2	5	4	5	1	3	4	2	2	4	1	5	3	3	5	1	2	4
20		1	4	5	3	2	4	5	1	3	2	4	5	2	3	1	4	1	5	3	2	1	2	4	3	5
21		3	5	4	2	1	1	4	5	2	3	1	4	5	2	3	3	5	4	2	1	4	3	5	1	2
22		3	2	5	1	4	4	3	1	2	5	1	2	3	4	5	1	3	2	5	4	2	4	3	1	5
23		1	5	3	4	2	5	1	4	3	2	5	4	1	2	3	4	5	1	3	2	1	2	5	3	4
24		2	1	4	5	3	1	2	5	4	3	3	1	4	5	2	3	2	5	4	1	3	1	4	5	2
25		5	4	2	3	1	3	5	2	1	4	2	3	5	1	4	5	1	4	2	3	4	5	1	2	3
26		4	3	1	2	5	2	4	3	5	1	4	5	2	3	1	2	4	3	1	5	5	3	2	4	1
27		2	1	4	5	3	1	4	2	3	5	5	2	3	1	4	2	1	4	3	5	4	3	5	1	2
28		4	2	5	3	1	2	3	1	5	4	2	1	4	3	5	3	4	5	1	2	3	5	1	2	4
29		3	5	2	1	4	4	5	3	2	1	4	3	1	5	2	4	2	3	5	1	1	4	2	3	5
30		1	4	3	2	5	3	1	5	4	2	1	4	5	2	3	1	5	2	4	3	2	1	4	5	3
31		5	3	1	4	2	5	2	4	1	3	3	5	2	4	1	5	3	1	2	4	5	2	3	4	1
32		3	1	2	5	4	5	1	3	4	2	2	1	4	3	5	5	3	4	1	2	3	4	5	1	2
33		1	5	3	4	2	2	3	1	5	4	5	4	3	2	1	3	5	2	4	1	4	1	3	2	5
34		5	2	4	1	3	4	2	5	3	1	1	2	5	4	3	2	1	3	5	4	1	3	2	5	4
35		2	4	5	3	1	1	5	4	2	3	3	5	2	1	4	1	4	5	2	3	5	2	1	4	3
36		4	3	1	2	5	3	4	2	1	5	4	3	1	5	2	4	2	1	3	5	2	5	4	3	1
37		4	5	3	2	1	2	5	4	3	1	2	1	3	4	5	5	1	4	2	3	5	3	1	2	4
38		5	2	4	1	3	5	3	2	1	4	5	4	1	3	2	3	2	1	4	5	4	1	5	3	2
39		1	3	5	4	2	1	4	3	2	5	3	5	2	1	4	1	5	2	3	4	3	2	4	5	1
40		3	1	2	5	4	4	2	1	5	3	1	2	4	5	3	4	3	5	1	2	2	4	3	1	5
41		2	4	1	3	5	3	1	5	4	2	4	3	5	2	1	2	4	3	5	1	1	5	2	4	3
42
Sheet1

Cell Formulas
Range	Formula
B2,B16	B2	=FORMULATEXT(B3)
B3:M14	B3	=NK(4,3,100)
B17:Z41	B17	=NK(5,5,1000)
Dynamic array formulas.

Lambda Functions
Name	Formula
NK	=LAMBDA(n,k,ni,LET(s,SEQUENCE(n),q,SEQUENCE(k),r,LAMBDA(n,TOROW(SORTBY(s,RANDARRAY(n)))),c,LAMBDA(x,AND(BYCOL(x,LAMBDA(y,ROWS(UNIQUE(y))=ROWS(x))))),b,LAMBDA(x,REDUCE(r(n),SEQUENCE(ni,3),LAMBDA(v,i,IF(ROWS(v)=x,v,LET(a,VSTACK(v,r(x)),IF(c(a),a,v)))))),DROP(REDUCE("",q,LAMBDA(v,i,VSTACK(v,DROP(REDUCE("",q,LAMBDA(v,i,HSTACK(v,b(n)))),,1)))),1)))

 

[Xlambda]

NKni.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O
1
2
3		checking: no dups byrow or by col for a single 8x8 array
4
5		=NK(8,1,100000)									=BYROW(B6#,LAMBDA(x,COUNT(UNIQUE(x,1))))
6		7	1	4	8	3	6	2	5		8
7		5	3	6	7	8	4	1	2		8
8		3	4	7	1	6	2	5	8		8
9		8	5	2	3	4	1	7	6		8
10		4	6	1	2	5	7	8	3		8
11		2	7	8	5	1	3	6	4		8
12		6	2	5	4	7	8	3	1		8
13		1	8	3	6	2	5	4	7		8
14
15		=BYCOL(B6#,LAMBDA(x,COUNT(UNIQUE(x))))
16		8	8	8	8	8	8	8	8
17
Sheet2

Cell Formulas
Range	Formula
B5,B15,K5	B5	=FORMULATEXT(B6)
B6:I13	B6	=NK(8,1,100000)
K6:K13	K6	=BYROW(B6#,LAMBDA(x,COUNT(UNIQUE(x,1))))
B16:I16	B16	=BYCOL(B6#,LAMBDA(x,COUNT(UNIQUE(x))))
Dynamic array formulas.

 

[MrExcel]

This is amazing - a collection of valid Sudoku grids!

 

[Xlambda]

This is amazing - a collection of valid Sudoku grids!

Glad you liked it. ✌
Remember we were talking about recursion limitations? Turns out it was some kind of a glitch.
Check this out, made a post about it here:

ARF

ARF !! recursive !! DIY Array Recursive Function kit. Idea triggered by an ExcelIsFun YT video posted yesterday EMT1744 (different topic) . Other functions on minisheet AFLAT. Other functions, never defined before, can be copied directly from minisheet APP and ASU, they follow same syntax as the...

www.mrexcel.com

 

[Xlambda]

This is amazing - a collection of valid Sudoku grids!

Ref: year 2025 cool formula. Posted a comment 5 days ago, seems that YT deleted it (or can be seen if we choose "Sort by "+"Newest first")
"
Yes, there are a lot of cool facts about this number. (45^2=2025) Another one:
if we write a continuous string, of all numbers from 1 to 45, repeating them by their value, (1 2 2 3 3 3 4 4 4 4…...) will get a huge number that will have …2025 digits.
These are cool facts because they are specific to 2025 only, pattern constructions can be done for any arrays.
Visual proof of all 2025 digits in an array of 45x45 , simplest single formula ever
=--MID(CONCAT(REPT(SEQUENCE(45),SEQUENCE(45))),SEQUENCE(45,45),1) ✌
"

Book1
	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	AC	AD	AE	AF	AG	AH	AI	AJ	AK	AL	AM	AN	AO	AP	AQ	AR	AS	AT	AU
1
2		=--MID(CONCAT(REPT(SEQUENCE(45),SEQUENCE(45))),SEQUENCE(45,45),1)
3		1	2	2	3	3	3	4	4	4	4	5	5	5	5	5	6	6	6	6	6	6	7	7	7	7	7	7	7	8	8	8	8	8	8	8	8	9	9	9	9	9	9	9	9	9
4		1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	2	1
5		2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3
6		1	3	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	5	1	5	1	5	1	5	1	5	1	5	1	5	1
7		5	1	5	1	5	1	5	1	5	1	5	1	5	1	5	1	6	1	6	1	6	1	6	1	6	1	6	1	6	1	6	1	6	1	6	1	6	1	6	1	6	1	6	1	6
8		1	6	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	7	1	8	1	8	1	8	1	8	1
9		8	1	8	1	8	1	8	1	8	1	8	1	8	1	8	1	8	1	8	1	8	1	8	1	8	1	8	1	9	1	9	1	9	1	9	1	9	1	9	1	9	1	9	1	9
10		1	9	1	9	1	9	1	9	1	9	1	9	1	9	1	9	1	9	1	9	2	0	2	0	2	0	2	0	2	0	2	0	2	0	2	0	2	0	2	0	2	0	2	0	2
11		0	2	0	2	0	2	0	2	0	2	0	2	0	2	0	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1
12		2	1	2	1	2	1	2	1	2	1	2	1	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2
13		2	2	2	2	2	2	2	2	2	2	2	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3
14		2	3	2	3	2	3	2	3	2	3	2	3	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2
15		4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5
16		2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	5	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2
17		6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	6	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7
18		2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	7	2	8	2	8	2	8	2	8	2
19		8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8	2	8
20		2	8	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	2
21		9	2	9	2	9	2	9	2	9	2	9	2	9	2	9	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0
22		3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	0	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3
23		1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1	3	1
24		3	1	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3
25		2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	2	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3
26		3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	4	3
27		4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4
28		3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3
29		5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5	3	5
30		3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3
31		6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	6	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7
32		3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3	7	3
33		7	3	7	3	7	3	7	3	7	3	7	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8
34		3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	8	3	9	3
35		9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9
36		3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	3	9	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4
37		0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0
38		4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	0	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4
39		1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1	4	1
40		4	1	4	1	4	1	4	1	4	1	4	1	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4
41		2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2	4	2
42		4	2	4	2	4	2	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4
43		3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3	4	3
44		4	3	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4
45		4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4
46		4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4
47		5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5	4	5
48
Sheet1

Cell Formulas
Range	Formula
B2	B2	=FORMULATEXT(B3)
B3:AT47	B3	=--MID(CONCAT(REPT(SEQUENCE(45),SEQUENCE(45))),SEQUENCE(45,45),1)
Dynamic array formulas.

Lambda Functions
Name	Formula
ND	=LAMBDA(n,LET(r,LAMBDA(SORTBY(SEQUENCE(n),RANDARRAY(n))),a,MOD(SEQUENCE(,n)-SEQUENCE(n),n)+1,INDEX(a,r(),TOROW(r()))))

Fun fact 2: Out of all perfect square years between (1,10000], 2025 is the only year that checks this fact.

Book1
	A	B	C	D	E	F	G	H	I	J	K	L
1		perf square
2		years btw.
3		1 - 10000
4		=LET(y,SEQUENCE(10000),m,MOD(SQRT(y),1)=0,FILTER(y,m))
5		↓↓		=MAP(B6#,LAMBDA(x,LET(q,SQRT(x),s,SEQUENCE(q),l,LEN(CONCAT(REPT(s,s))),l-x)))
6		1		0
7		4		-1
8		9		-3
9		16		-6
10		25		-10
11		36		-15
12		49		-21
13		64		-28
14		81		-36
15		100		-35
16		121		-34
17		144		-33
18		169		-32
19		196		-31
20		225		-30
21		256		-29
22		289		-28
23		324		-27
24		361		-26
25		400		-25
26		441		-24
27		484		-23
28		529		-22
29		576		-21
30		625		-20
31		676		-19
32		729		-18
33		784		-17
34		841		-16
35		900		-15
36		961		-14
37		1024		-13
38		1089		-12
39		1156		-11
40		1225		-10
41		1296		-9
42		1369		-8
43		1444		-7
44		1521		-6
45		1600		-5
46		1681		-4
47		1764		-3
48		1849		-2
49		1936		-1
50		2025		0
51		2116		1
52		2209		2
53		2304		3
54		2401		4
55		2500		5
56		2601		6
57		2704		7
58		2809		8
59		2916		9
60		3025		10
61		3136		11
62		3249		12
63		3364		13
64		3481		14
65		3600		15
66		3721		16
67		3844		17
68		3969		18
69		4096		19
70		4225		20
71		4356		21
72		4489		22
73		4624		23
74		4761		24
75		4900		25
76		5041		26
77		5184		27
78		5329		28
79		5476		29
80		5625		30
81		5776		31
82		5929		32
83		6084		33
84		6241		34
85		6400		35
86		6561		36
87		6724		37
88		6889		38
89		7056		39
90		7225		40
91		7396		41
92		7569		42
93		7744		43
94		7921		44
95		8100		45
96		8281		46
97		8464		47
98		8649		48
99		8836		49
100		9025		50
101		9216		51
102		9409		52
103		9604		53
104		9801		54
105		10000		155
106
Sheet3

Cell Formulas
Range	Formula
B4	B4	=FORMULATEXT(B6)
D5	D5	=FORMULATEXT(D6)
B6:B105	B6	=LET(y,SEQUENCE(10000),m,MOD(SQRT(y),1)=0,FILTER(y,m))
D6:D105	D6	=MAP(B6#,LAMBDA(x,LET(q,SQRT(x),s,SEQUENCE(q),l,LEN(CONCAT(REPT(s,s))),l-x)))
Dynamic array formulas.

Lambda Functions
Name	Formula
ND	=LAMBDA(n,LET(r,LAMBDA(SORTBY(SEQUENCE(n),RANDARRAY(n))),a,MOD(SEQUENCE(,n)-SEQUENCE(n),n)+1,INDEX(a,r(),TOROW(r()))))

 

[Xlambda]

Also I thought it would be cool to write a random array of 45x45 with numbers that do not repeat byrow/bycol.
Here is a simple lambda that can deliver a random square array of n x n numbers [1-n], that do not repeat byrow/bycol, => no dups byrow nor bycol.
ND( n) No Dups function

=LAMBDA(n,
    LET(
        r, LAMBDA(SORTBY(SEQUENCE(n), RANDARRAY(n))),
        a, MOD(SEQUENCE(, n) - SEQUENCE(n), n) + 1,
        INDEX(a, r(), TOROW(r()))
    )
)

Book1
	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	AC	AD	AE	AF	AG	AH	AI	AJ	AK	AL	AM	AN	AO	AP	AQ	AR	AS	AT	AU	AV	AW	AX	AY	AZ	BA	BB	BC
1		=ND(45)
2		32	36	30	5	12	14	44	23	26	19	10	37	3	31	27	4	38	25	16	6	9	45	29	28	13	43	34	21	39	22	33	1	40	8	18	24	11	20	41	42	17	2	35	7	15
3		28	32	26	1	8	10	40	19	22	15	6	33	44	27	23	45	34	21	12	2	5	41	25	24	9	39	30	17	35	18	29	42	36	4	14	20	7	16	37	38	13	43	31	3	11		checking no dups (45 uniques byrow and bycol for each row/col => no dups)
4		6	10	4	24	31	33	18	42	45	38	29	11	22	5	1	23	12	44	35	25	28	19	3	2	32	17	8	40	13	41	7	20	14	27	37	43	30	39	15	16	36	21	9	26	34
5		27	31	25	45	7	9	39	18	21	14	5	32	43	26	22	44	33	20	11	1	4	40	24	23	8	38	29	16	34	17	28	41	35	3	13	19	6	15	36	37	12	42	30	2	10		=AND(BYCOL(B2#,LAMBDA(x,ROWS(UNIQUE(x))=45)))
6		36	40	34	9	16	18	3	27	30	23	14	41	7	35	31	8	42	29	20	10	13	4	33	32	17	2	38	25	43	26	37	5	44	12	22	28	15	24	45	1	21	6	39	11	19		TRUE
7		25	29	23	43	5	7	37	16	19	12	3	30	41	24	20	42	31	18	9	44	2	38	22	21	6	36	27	14	32	15	26	39	33	1	11	17	4	13	34	35	10	40	28	45	8
8		31	35	29	4	11	13	43	22	25	18	9	36	2	30	26	3	37	24	15	5	8	44	28	27	12	42	33	20	38	21	32	45	39	7	17	23	10	19	40	41	16	1	34	6	14		=AND(BYROW(B2#,LAMBDA(x,ROWS(UNIQUE(TOCOL(x)))=45)))
9		21	25	19	39	1	3	33	12	15	8	44	26	37	20	16	38	27	14	5	40	43	34	18	17	2	32	23	10	28	11	22	35	29	42	7	13	45	9	30	31	6	36	24	41	4		TRUE
10		2	6	45	20	27	29	14	38	41	34	25	7	18	1	42	19	8	40	31	21	24	15	44	43	28	13	4	36	9	37	3	16	10	23	33	39	26	35	11	12	32	17	5	22	30
11		8	12	6	26	33	35	20	44	2	40	31	13	24	7	3	25	14	1	37	27	30	21	5	4	34	19	10	42	15	43	9	22	16	29	39	45	32	41	17	18	38	23	11	28	36
12		13	17	11	31	38	40	25	4	7	45	36	18	29	12	8	30	19	6	42	32	35	26	10	9	39	24	15	2	20	3	14	27	21	34	44	5	37	1	22	23	43	28	16	33	41
13		1	5	44	19	26	28	13	37	40	33	24	6	17	45	41	18	7	39	30	20	23	14	43	42	27	12	3	35	8	36	2	15	9	22	32	38	25	34	10	11	31	16	4	21	29
14		19	23	17	37	44	1	31	10	13	6	42	24	35	18	14	36	25	12	3	38	41	32	16	15	45	30	21	8	26	9	20	33	27	40	5	11	43	7	28	29	4	34	22	39	2
15		33	37	31	6	13	15	45	24	27	20	11	38	4	32	28	5	39	26	17	7	10	1	30	29	14	44	35	22	40	23	34	2	41	9	19	25	12	21	42	43	18	3	36	8	16
16		7	11	5	25	32	34	19	43	1	39	30	12	23	6	2	24	13	45	36	26	29	20	4	3	33	18	9	41	14	42	8	21	15	28	38	44	31	40	16	17	37	22	10	27	35
17		22	26	20	40	2	4	34	13	16	9	45	27	38	21	17	39	28	15	6	41	44	35	19	18	3	33	24	11	29	12	23	36	30	43	8	14	1	10	31	32	7	37	25	42	5
18		41	45	39	14	21	23	8	32	35	28	19	1	12	40	36	13	2	34	25	15	18	9	38	37	22	7	43	30	3	31	42	10	4	17	27	33	20	29	5	6	26	11	44	16	24
19		4	8	2	22	29	31	16	40	43	36	27	9	20	3	44	21	10	42	33	23	26	17	1	45	30	15	6	38	11	39	5	18	12	25	35	41	28	37	13	14	34	19	7	24	32
20		45	4	43	18	25	27	12	36	39	32	23	5	16	44	40	17	6	38	29	19	22	13	42	41	26	11	2	34	7	35	1	14	8	21	31	37	24	33	9	10	30	15	3	20	28
21		26	30	24	44	6	8	38	17	20	13	4	31	42	25	21	43	32	19	10	45	3	39	23	22	7	37	28	15	33	16	27	40	34	2	12	18	5	14	35	36	11	41	29	1	9
22		34	38	32	7	14	16	1	25	28	21	12	39	5	33	29	6	40	27	18	8	11	2	31	30	15	45	36	23	41	24	35	3	42	10	20	26	13	22	43	44	19	4	37	9	17
23		5	9	3	23	30	32	17	41	44	37	28	10	21	4	45	22	11	43	34	24	27	18	2	1	31	16	7	39	12	40	6	19	13	26	36	42	29	38	14	15	35	20	8	25	33
24		20	24	18	38	45	2	32	11	14	7	43	25	36	19	15	37	26	13	4	39	42	33	17	16	1	31	22	9	27	10	21	34	28	41	6	12	44	8	29	30	5	35	23	40	3
25		15	19	13	33	40	42	27	6	9	2	38	20	31	14	10	32	21	8	44	34	37	28	12	11	41	26	17	4	22	5	16	29	23	36	1	7	39	3	24	25	45	30	18	35	43
26		9	13	7	27	34	36	21	45	3	41	32	14	25	8	4	26	15	2	38	28	31	22	6	5	35	20	11	43	16	44	10	23	17	30	40	1	33	42	18	19	39	24	12	29	37
27		24	28	22	42	4	6	36	15	18	11	2	29	40	23	19	41	30	17	8	43	1	37	21	20	5	35	26	13	31	14	25	38	32	45	10	16	3	12	33	34	9	39	27	44	7
28		11	15	9	29	36	38	23	2	5	43	34	16	27	10	6	28	17	4	40	30	33	24	8	7	37	22	13	45	18	1	12	25	19	32	42	3	35	44	20	21	41	26	14	31	39
29		29	33	27	2	9	11	41	20	23	16	7	34	45	28	24	1	35	22	13	3	6	42	26	25	10	40	31	18	36	19	30	43	37	5	15	21	8	17	38	39	14	44	32	4	12
30		37	41	35	10	17	19	4	28	31	24	15	42	8	36	32	9	43	30	21	11	14	5	34	33	18	3	39	26	44	27	38	6	45	13	23	29	16	25	1	2	22	7	40	12	20
31		10	14	8	28	35	37	22	1	4	42	33	15	26	9	5	27	16	3	39	29	32	23	7	6	36	21	12	44	17	45	11	24	18	31	41	2	34	43	19	20	40	25	13	30	38
32		40	44	38	13	20	22	7	31	34	27	18	45	11	39	35	12	1	33	24	14	17	8	37	36	21	6	42	29	2	30	41	9	3	16	26	32	19	28	4	5	25	10	43	15	23
33		23	27	21	41	3	5	35	14	17	10	1	28	39	22	18	40	29	16	7	42	45	36	20	19	4	34	25	12	30	13	24	37	31	44	9	15	2	11	32	33	8	38	26	43	6
34		39	43	37	12	19	21	6	30	33	26	17	44	10	38	34	11	45	32	23	13	16	7	36	35	20	5	41	28	1	29	40	8	2	15	25	31	18	27	3	4	24	9	42	14	22
35		12	16	10	30	37	39	24	3	6	44	35	17	28	11	7	29	18	5	41	31	34	25	9	8	38	23	14	1	19	2	13	26	20	33	43	4	36	45	21	22	42	27	15	32	40
36		38	42	36	11	18	20	5	29	32	25	16	43	9	37	33	10	44	31	22	12	15	6	35	34	19	4	40	27	45	28	39	7	1	14	24	30	17	26	2	3	23	8	41	13	21
37		43	2	41	16	23	25	10	34	37	30	21	3	14	42	38	15	4	36	27	17	20	11	40	39	24	9	45	32	5	33	44	12	6	19	29	35	22	31	7	8	28	13	1	18	26
38		18	22	16	36	43	45	30	9	12	5	41	23	34	17	13	35	24	11	2	37	40	31	15	14	44	29	20	7	25	8	19	32	26	39	4	10	42	6	27	28	3	33	21	38	1
39		17	21	15	35	42	44	29	8	11	4	40	22	33	16	12	34	23	10	1	36	39	30	14	13	43	28	19	6	24	7	18	31	25	38	3	9	41	5	26	27	2	32	20	37	45
40		30	34	28	3	10	12	42	21	24	17	8	35	1	29	25	2	36	23	14	4	7	43	27	26	11	41	32	19	37	20	31	44	38	6	16	22	9	18	39	40	15	45	33	5	13
41		3	7	1	21	28	30	15	39	42	35	26	8	19	2	43	20	9	41	32	22	25	16	45	44	29	14	5	37	10	38	4	17	11	24	34	40	27	36	12	13	33	18	6	23	31
42		44	3	42	17	24	26	11	35	38	31	22	4	15	43	39	16	5	37	28	18	21	12	41	40	25	10	1	33	6	34	45	13	7	20	30	36	23	32	8	9	29	14	2	19	27
43		16	20	14	34	41	43	28	7	10	3	39	21	32	15	11	33	22	9	45	35	38	29	13	12	42	27	18	5	23	6	17	30	24	37	2	8	40	4	25	26	1	31	19	36	44
44		35	39	33	8	15	17	2	26	29	22	13	40	6	34	30	7	41	28	19	9	12	3	32	31	16	1	37	24	42	25	36	4	43	11	21	27	14	23	44	45	20	5	38	10	18
45		42	1	40	15	22	24	9	33	36	29	20	2	13	41	37	14	3	35	26	16	19	10	39	38	23	8	44	31	4	32	43	11	5	18	28	34	21	30	6	7	27	12	45	17	25
46		14	18	12	32	39	41	26	5	8	1	37	19	30	13	9	31	20	7	43	33	36	27	11	10	40	25	16	3	21	4	15	28	22	35	45	6	38	2	23	24	44	29	17	34	42
47
Sheet2

Cell Formulas
Range	Formula
B1,AV8,AV5	B1	=FORMULATEXT(B2)
B2:AT46	B2	=ND(45)
AV6	AV6	=AND(BYCOL(B2#,LAMBDA(x,ROWS(UNIQUE(x))=45)))
AV9	AV9	=AND(BYROW(B2#,LAMBDA(x,ROWS(UNIQUE(TOCOL(x)))=45)))
Dynamic array formulas.

Lambda Functions
Name	Formula
ND	=LAMBDA(n,LET(r,LAMBDA(SORTBY(SEQUENCE(n),RANDARRAY(n))),a,MOD(SEQUENCE(,n)-SEQUENCE(n),n)+1,INDEX(a,r(),TOROW(r()))))