ARF

[Xlambda]

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 "kit".
If a function (F) (build in or custom made), applied to an array (a), returns a single value or a horizontal 1D array (v), F(a)=v, then, ARF((a1,a2,…an),,)={F(a1);F(a2);…;F(an)}={v1;v2…;vn}
ARF(a,ai,i)=LAMBDA(a,ai,i,LET(n,AREAS(a),s,SEQUENCE( n),j,IF(i="",n,i),x,INDEX(a,,,j),IF(j=0,ai,ARF(a,IF(s=j,F(x),ai),j-1))))
a: (a1,a2,…,an), non-adjacent ranges on same sheet, enclosed in parentheses like in 2nd syntax of INDEX function INDEX(reference, row_num, [column_num], [area_num])
ai,i: initial values always ignored, (,,) have the role of "vector carriers"
If F has one or more arguments F(a,k) : (I will cover more complex examples as soon as I will have some spare time)
ARF(a,k,ai,i)=LAMBDA(a,k,ai,i,LET(n,AREAS(a),s,SEQUENCE( n),j,IF(i="",n,i),x,INDEX(a,,,j),IF(j=0,ai,ARF(a,k,IF(s=j,F(x,k),ai),j-1))))

AGG study.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S
1	Base Case example (simplest case scenario): append arrays (single cell , or 1D horizontal arrays)
2	Note: We don't need more functionality since the functions will return single values or horizontal 1D arrays, keeping the kits construction as simple as possible
3	To append 2D arrays we already have					APPENDNHV
4	Writing the recursive function following the syntax draft, function name, let's define APP:
5	APP(a,ai,i)=LAMBDA(a,ai,i,LET(n,AREAS(a),s,SEQUENCE(n),j,IF(i="",n,i),x,INDEX(a,,,j),IF(j=0,ai,APP(a,IF(s=j,x,ai),j-1))))
6	The appending "engine" functionality is extremely simple IF(s=j,x,ai)
7	Is equivalent with this :
8	=LET(s,SEQUENCE(3),SWITCH(s,1,"a",2,"b",3,2))
9	a
10	b		a1				=APP((C11:D11,C14:E14,C17:D17),,)
11	2		a	2			a	2	#N/A
12							b	3	4
13			a2				1	2	#N/A
14			b	3	4
15
16			a3
17			1	2
18
19	General Case example: let's consider a more complex F(x) that sorts in ascending order the unique elements of an array
20		a1
21		a	2	3			=TRANSPOSE(SORT(UNIQUE(AFLAT(B21:D23))))
22		x	w	2			2	3	a	t	w	x
23		t	x	a
24
25	so F(x) will be F(x)=TRANSPOSE(SORT(UNIQUE(AFLAT(x))))
26	Now let's define our specific recursive function (ASU) using the kit syntax
27	ASU(a,ai,i)=LAMBDA(a,ai,i,LET(n,AREAS(a),s,SEQUENCE(n),j,IF(i="",n,i),x,INDEX(a,,,j),IF(j=0,IFERROR(ai,""),ASU(a,IF(s=j,TRANSPOSE(SORT(UNIQUE(AFLAT(x)))),ai),j-1))))
28		a2
29		a	2	-1			=ASU((B21:D23,B29:D33,B36:C37),,)
30		q	a	c			2	3	a	t	w	x
31		d	c	2			-1	2	3	a	c	d	q
32		-1	3	-1			2	q
33		2	d	d
34
35		a3					Other function on minisheet
36		q	2				AFLAT
37		2	q
38
39	This proves the functionality of the kit, whatever function we can use to calculate an array and return a single cell result or 1D horiz array, can be done recursively to many arrays using the kit.
40	It will be nice to see others function creations posted here!!!
41
ARF post

Cell Formulas
Range	Formula
A8,G29,G21,G10	A8	=FORMULATEXT(A9)
A9:A11	A9	=LET(s,SEQUENCE(3),SWITCH(s,1,"a",2,"b",3,2))
G11:I13	G11	=APP((C11:D11,C14:E14,C17:D17),,)
G22:L22	G22	=TRANSPOSE(SORT(UNIQUE(AFLAT(B21:D23))))
G30:M32	G30	=ASU((B21:D23,B29:D33,B36:C37),,)
Dynamic array formulas.

 

[smozgur]

FYI: Another video from MrExcel about the new functions:

PRODUCTIF With MAP REDUCE or SCAN - 2416

Three more of the new Lambda Helper functions in Excel: MAP, REDUCE, and SCAN. In today's episode, see three different ways to create a PRODUCTIF function in Excel using MAP, REDUCE, or SCAN. Important points: MAP can take one or more arrays. MAP is looking at each individual cell, not just the...

www.mrexcel.com

 

[Xlambda]

FYI: Another video from MrExcel about the new functions:

PRODUCTIF With MAP REDUCE or SCAN - 2416

Three more of the new Lambda Helper functions in Excel: MAP, REDUCE, and SCAN. In today's episode, see three different ways to create a PRODUCTIF function in Excel using MAP, REDUCE, or SCAN. Important points: MAP can take one or more arrays. MAP is looking at each individual cell, not just the...

www.mrexcel.com

Hi, kind of off-topic here, but I think it worth mentioning, wrote the first lambda ( AGGR AGGR(a,fn,[kn]) with an optional argument "[kn]" and I have noticed that array syntax field, (very first row) does not accept brackets.
Function arguments field works fine, took the brackets. ✌

 

[smozgur]

Hi, kind of off-topic here, but I think it worth mentioning, wrote the first lambda ( AGGR AGGR(a,fn,[kn]) with an optional argument "[kn]" and I have noticed that array syntax field, (very first row) does not accept brackets.
Function arguments field works fine, took the brackets. ✌

Thanks for the heads up. I just made the necessary changes to allow brackets and edited the AGGR function post.

 

[Xlambda]

Check this out, another cool excel challenge from today's Jon-Excel Campus YT: Excel Formula Challenge: Even or Odd License Plates
I was missing the "elegance" of recursive functions.
EO(c) Even/Odd function. recursive !!!
c: single value, single cell reference

=LAMBDA(c,
    LET(
        n, LEN(c),
        x, --RIGHT(c, 1),
        IF(n = 0, "Odd", IF(ISERR(x), EO(LEFT(c, n - 1)), IF(ISODD(x), "Odd", "Even")))
    )
)

Excel-Challenge-License-Plates.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O
1	License Plate Challenge			Rule: If last digit of license plate is odd nr. than "Odd", else "Even", if no digits found => "Odd"
2		1st solution		2nd solution, entire clm vector, all steps
3				=REDUCE(A6:A55,CHAR(SEQUENCE(26,,65)),LAMBDA(v,x,SUBSTITUTE(v,x,"")))
4		=EO([@[Plate Number]])		↓↓↓		=--RIGHT(D6#,1)		=IF(ISODD(+F6#),"Odd","Even")
5	Plate Number	Odd/Even		↓↓↓		↓↓↓		↓↓↓		=IFERROR(H6#,"Odd")
6	123M57	Odd		12357		7		Odd		Odd
7	1COU886	Even		1886		6		Even		Even		check results, both solutions
8	1D48821	Odd		148821		1		Odd		Odd		=AND(J6#=tblChallenge[Odd/Even])
9	1DVT189	Odd		1189		9		Odd		Odd		TRUE
10	21W7454	Even		217454		4		Even		Even
11	27U17	Odd		2717		7		Odd		Odd
12	2IGR878	Even		2878		8		Even		Even
13	2RDZ434	Even		2434		4		Even		Even
14	2SWQ185	Odd		2185		5		Odd		Odd
15	3FII697	Odd		3697		7		Odd		Odd
16	3QOW866	Even		3866		6		Even		Even
17	3RQC229	Odd		3229		9		Odd		Odd
18	3RSZ114	Even		3114		4		Even		Even
19	4FXL296	Even		4296		6		Even		Even
20	4KUC981	Odd		4981		1		Odd		Odd
21	4QKB212	Even		4212		2		Even		Even
22	4QRG241	Odd		4241		1		Odd		Odd
23	4RVF139	Odd		4139		9		Odd		Odd
24	5ACY568	Even		5568		8		Even		Even
25	5IYF234	Even		5234		4		Even		Even
26	5KFC128	Even		5128		8		Even		Even
27	5NFD419	Odd		5419		9		Odd		Odd
28	5RXA984	Even		5984		4		Even		Even
29	5TGB871	Odd		5871		1		Odd		Odd
30	5UEZ777	Odd		5777		7		Odd		Odd
31	5WKT763	Odd		5763		3		Odd		Odd
32	6LJT722	Even		6722		2		Even		Even
33	6MVB117	Odd		6117		7		Odd		Odd
34	6XZR265	Odd		6265		5		Odd		Odd
35	71F27UJ	Odd		7127		7		Odd		Odd
36	745Y4I	Even		7454		4		Even		Even
37	76736Q	Even		76736		6		Even		Even
38	7FOB933	Odd		7933		3		Odd		Odd
39	7JCM371	Odd		7371		1		Odd		Odd
40	884PCX	Even		884		4		Even		Even
41	8JHC777	Odd		8777		7		Odd		Odd
42	8RDQ178	Even		8178		8		Even		Even
43	8TMW513	Odd		8513		3		Odd		Odd
44	9PMH329	Odd		9329		9		Odd		Odd
45	9UGW414	Even		9414		4		Even		Even
46	9UUL349	Odd		9349		9		Odd		Odd
47	BEACH	Odd				#VALUE!		#VALUE!		Odd
48	G97C8T	Even		978		8		Even		Even
49	H1R226I	Even		1226		6		Even		Even
50	KL7469C	Odd		7469		9		Odd		Odd
51	RUSS	Odd				#VALUE!		#VALUE!		Odd
52	S94CO	Even		94		4		Even		Even
53	T5A5MEN	Odd		55		5		Odd		Odd
54	YELOSTN	Odd				#VALUE!		#VALUE!		Odd
55	YOSEMIT	Odd				#VALUE!		#VALUE!		Odd
56
Challenge

Cell Formulas
Range	Formula
D3	D3	=FORMULATEXT(D6)
B4,F4,H4	B4	=FORMULATEXT(B6)
J5,L8	J5	=FORMULATEXT(J6)
D6:D55	D6	=REDUCE(A6:A55,CHAR(SEQUENCE(26,,65)),LAMBDA(v,x,SUBSTITUTE(v,x,"")))
F6:F55	F6	=--RIGHT(D6#,1)
H6:H55	H6	=IF(ISODD(+F6#),"Odd","Even")
J6:J55	J6	=IFERROR(H6#,"Odd")
L9	L9	=AND(J6#=tblChallenge[Odd/Even])
B6:B55	B6	=EO([@[Plate Number]])
Dynamic array formulas.

 

[Xlambda]

Array format, single cell formulas, 2 solutions, using recursive EO(c) and REDUCE

Excel-Challenge-License-Plates.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q
1				1 solution, using EO(c)
2				=MAP(B5:B54,LAMBDA(x,EO(x)))
3				↓↓↓		2 solution REDUCE, lambda formula
4		array		↓↓↓		=IFERROR(IF(ISODD(--RIGHT(REDUCE(B5:B54,CHAR(SEQUENCE(26,,65)),LAMBDA(v,x,SUBSTITUTE(v,x,""))),1)),"Odd","Even"),"Odd")
5		123M57		Odd		Odd
6		1COU886		Even		Even		check results, both solutions
7		1D48821		Odd		Odd		=AND(F5#=D5#)
8		1DVT189		Odd		Odd		TRUE
9		21W7454		Even		Even
10		27U17		Odd		Odd
11		2IGR878		Even		Even
12		2RDZ434		Even		Even
13		2SWQ185		Odd		Odd
14		3FII697		Odd		Odd
15		3QOW866		Even		Even
16		3RQC229		Odd		Odd
17		3RSZ114		Even		Even
18		4FXL296		Even		Even
19		4KUC981		Odd		Odd
20		4QKB212		Even		Even
21		4QRG241		Odd		Odd
22		4RVF139		Odd		Odd
23		5ACY568		Even		Even
24		5IYF234		Even		Even
25		5KFC128		Even		Even
26		5NFD419		Odd		Odd
27		5RXA984		Even		Even
28		5TGB871		Odd		Odd
29		5UEZ777		Odd		Odd
30		5WKT763		Odd		Odd
31		6LJT722		Even		Even
32		6MVB117		Odd		Odd
33		6XZR265		Odd		Odd
34		71F27UJ		Odd		Odd
35		745Y4I		Even		Even
36		76736Q		Even		Even
37		7FOB933		Odd		Odd
38		7JCM371		Odd		Odd
39		884PCX		Even		Even
40		8JHC777		Odd		Odd
41		8RDQ178		Even		Even
42		8TMW513		Odd		Odd
43		9PMH329		Odd		Odd
44		9UGW414		Even		Even
45		9UUL349		Odd		Odd
46		BEACH		Odd		Odd
47		G97C8T		Even		Even
48		H1R226I		Even		Even
49		KL7469C		Odd		Odd
50		RUSS		Odd		Odd
51		S94CO		Even		Even
52		T5A5MEN		Odd		Odd
53		YELOSTN		Odd		Odd
54		YOSEMIT		Odd		Odd
55
Challenge 2

Cell Formulas
Range	Formula
D2	D2	=FORMULATEXT(D5)
F4,H7	F4	=FORMULATEXT(F5)
D5:D54	D5	=MAP(B5:B54,LAMBDA(x,EO(x)))
F5:F54	F5	=IFERROR(IF(ISODD(--RIGHT(REDUCE(B5:B54,CHAR(SEQUENCE(26,,65)),LAMBDA(v,x,SUBSTITUTE(v,x,""))),1)),"Odd","Even"),"Odd")
H8	H8	=AND(F5#=D5#)
Dynamic array formulas.

 

[Xlambda]

For fun, let's create our own License Plate Generator.

Excel-Challenge-License-Plates.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		Concept. Creating 30 random license plates , letters and numbers, 7 chars long.
2		Formula trick to give digits close probability as letters have, to be picked up by random engine.(2 sequences of digits 0 to 9) (20 digits+ 26 letters=> sequence dimension=46)
3		↓↓↓
4		=LET(a,SEQUENCE(46,,65),IF(a>90,RIGHT(a,1),CHAR(a)))																		=BYROW(L6#,LAMBDA(x,TEXTJOIN(,,x)))
5		↓↓↓		=RANDARRAY(30,7,1,46,1)								=INDEX(B6#,D6#)								↓↓↓		=MAP(T6#,LAMBDA(x,EO(x)))
6		A		23	6	12	17	14	19	35		W	F	L	Q	N	S	9		WFLQNS9		Odd
7		B		4	38	6	8	8	38	8		D	2	F	H	H	2	H		D2FHH2H		Even
8		C		7	44	19	17	18	14	43		G	8	S	Q	R	N	7		G8SQRN7		Odd
9		D		27	4	29	22	12	7	7		1	D	3	V	L	G	G		1D3VLGG		Odd
10		E		12	14	37	24	7	1	10		L	N	1	X	G	A	J		LN1XGAJ		Odd
11		F		40	2	31	23	40	46	24		4	B	5	W	4	0	X		4B5W40X		Even
12		G		36	42	31	17	37	33	22		0	6	5	Q	1	7	V		065Q17V		Odd
13		H		27	40	17	5	15	38	33		1	4	Q	E	O	2	7		14QEO27		Odd
14		I		13	25	36	33	12	6	22		M	Y	0	7	L	F	V		MY07LFV		Odd
15		J		21	4	20	25	37	9	2		U	D	T	Y	1	I	B		UDTY1IB		Odd
16		K		33	30	33	16	44	26	30		7	4	7	P	8	Z	4		747P8Z4		Even
17		L		33	17	14	3	4	46	4		7	Q	N	C	D	0	D		7QNCD0D		Even
18		M		17	21	22	35	2	32	36		Q	U	V	9	B	6	0		QUV9B60		Even
19		N		43	10	16	39	29	45	27		7	J	P	3	3	9	1		7JP3391		Odd
20		O		7	21	14	19	41	32	5		G	U	N	S	5	6	E		GUNS56E		Even
21		P		16	36	10	36	7	4	28		P	0	J	0	G	D	2		P0J0GD2		Even
22		Q		6	3	40	12	2	4	43		F	C	4	L	B	D	7		FC4LBD7		Odd
23		R		25	40	29	35	38	7	23		Y	4	3	9	2	G	W		Y4392GW		Even
24		S		31	17	21	22	1	26	16		5	Q	U	V	A	Z	P		5QUVAZP		Odd
25		T		45	8	45	24	44	35	15		9	H	9	X	8	9	O		9H9X89O		Odd
26		U		10	40	18	28	38	24	21		J	4	R	2	2	X	U		J4R22XU		Even
27		V		31	24	32	38	14	46	33		5	X	6	2	N	0	7		5X62N07		Odd
28		W		44	19	37	45	30	27	12		8	S	1	9	4	1	L		8S1941L		Odd
29		X		9	32	10	13	18	35	9		I	6	J	M	R	9	I		I6JMR9I		Odd
30		Y		14	30	9	19	3	13	37		N	4	I	S	C	M	1		N4ISCM1		Odd
31		Z		13	37	24	9	39	16	41		M	1	X	I	3	P	5		M1XI3P5		Odd
32		1		16	9	13	8	32	19	20		P	I	M	H	6	S	T		PIMH6ST		Even
33		2		22	42	19	29	45	36	19		V	6	S	3	9	0	S		V6S390S		Even
34		3		45	9	39	32	20	46	1		9	I	3	6	T	0	A		9I36T0A		Even
35		4		18	2	4	36	12	24	22		R	B	D	0	L	X	V		RBD0LXV		Even
36		5
Lic Plt Gen 1

Cell Formulas
Range	Formula
B4,T4	B4	=FORMULATEXT(B6)
D5,V5,L5	D5	=FORMULATEXT(D6)
B6:B51	B6	=LET(a,SEQUENCE(46,,65),IF(a>90,RIGHT(a,1),CHAR(a)))
D6:J35	D6	=RANDARRAY(30,7,1,46,1)
L6:R35	L6	=INDEX(B6#,D6#)
T6:T35	T6	=BYROW(L6#,LAMBDA(x,TEXTJOIN(,,x)))
V6:V35	V6	=MAP(T6#,LAMBDA(x,EO(x)))
Dynamic array formulas.

 

[Xlambda]

Excel-Challenge-License-Plates.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M
1		Single cell formula. Creating n random license plates , letters and numbers, 7 chars long.
2
3		n	40
4
5		=LET(n,C3,s,SEQUENCE(46,,65),q,IF(s>90,RIGHT(s,1),CHAR(s)),BYROW(INDEX(q,RANDARRAY(n,7,1,46,1)),LAMBDA(x,TEXTJOIN(,,x))))
6		↓↓↓
7		↓↓↓				=MAP(B8#,LAMBDA(x,EO(x)))
8		IX6KG32		check n		Even
9		RRBVZB3		=ROWS(B8#)		Odd
10		D2N300Z		40		Even
11		G82NVPI				Even
12		NDT0OC7				Odd
13		TZ746G5				Odd
14		O69H5SR				Odd
15		H4N3O01				Odd
16		Q8DV0X0				Even
17		EPT4Y9Q				Odd
18		V2DCW97				Odd
19		075BN3S				Odd
20		VL91WO5				Odd
21		R88Q8S8				Even
22		J09DA3Y				Odd
23		5W0WC6Z				Even
24		BYJZA99				Odd
25		1152JW7				Odd
26		RN02CJH				Even
27		7HZJ63F				Odd
28		5YIES07				Odd
29		GKLX394				Even
30		K8BTN0C				Even
31		OP36E8D				Even
32		NSZZ0OU				Even
33		15R24C8				Even
34		BT04CDG				Even
35		1F4F6N1				Odd
36		51M1607				Odd
37		W2YJZ5N				Odd
38		0RA3198				Even
39		CP6MRY8				Even
40		V10B538				Even
41		7KROR03				Odd
42		7O837O3				Odd
43		A31Z6SU				Even
44		692MXHD				Even
45		4P1QMS3				Odd
46		0JW209R				Odd
47		2MX23IC				Odd
48
Lic Plt Gen 2

Cell Formulas
Range	Formula
B5	B5	=FORMULATEXT(B8)
F7,D9	F7	=FORMULATEXT(F8)
B8:B47	B8	=LET(n,C3,s,SEQUENCE(46,,65),q,IF(s>90,RIGHT(s,1),CHAR(s)),BYROW(INDEX(q,RANDARRAY(n,7,1,46,1)),LAMBDA(x,TEXTJOIN(,,x))))
F8:F47	F8	=MAP(B8#,LAMBDA(x,EO(x)))
D10	D10	=ROWS(B8#)
Dynamic array formulas.

 

[Xlambda]

Excel-Challenge-License-Plates.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T
1		Single cell formula. Creating n random license plates , letters and numbers, min 5 max 7 chars long. More licenses should have 7 characters.
2		This time licenses will contain more digits than previous examples => will use ...s,SEQUENCE(66,,65)…(26 letters and 4 sequences 0-9 => sequence dimention = 26+40=66)
3
4		n	32
5
6		all 7 chars long strings
7		=LET(n,C4,s,SEQUENCE(66,,65),q,IF(s>90,RIGHT(s,1),CHAR(s)),BYROW(INDEX(q,RANDARRAY(n,7,1,66,1)),LAMBDA(x,TEXTJOIN(,,x))))
8		↓↓↓		random gen nr. btw 5 and 7
9		↓↓↓		Trick formula to deliver more of 7 chars than 5 or 6
10		↓↓↓		=LET(d,RANDARRAY(C4,,5,10,1),IF(d>7,7,d))
11		↓↓↓		↓↓↓		=LEFT(B12#,D12#)		5,6,7 chars		I11:								=MAP(H12#,LAMBDA(x,EO(x)))
12		T4GBBO4		7		T4GBBO4		18BC031	←←←	=LET(n,C4, s,SEQUENCE(66,,65), q,IF(s>90,RIGHT(s,1),CHAR(s)), b,BYROW(INDEX(q,RANDARRAY(n,7,1,66,1)),LAMBDA(x,TEXTJOIN(,,x))), d,RANDARRAY(n,,5,10,1), LEFT(b,IF(d>7,7,d)))								Odd
13		MU88EW4		7		MU88EW4		20204										Even
14		98X94M3		7		98X94M3		1G079L8										Even
15		K6V9060		7		K6V9060		10U9Q7X										Odd
16		95XE64G		7		95XE64G		AA142T2										Even
17		QZF29NL		6		QZF29N		3M6CL										Even
18		670X4TF		7		670X4TF		Q3190										Even
19		S8RA7Q3		5		S8RA7		6DE9QR8										Even
20		RFHS0FI		7		RFHS0FI		41PZ6M		Tasks accomplished:								Even
21		948N637		7		948N637		K5A8FZ8		On average, licenses have more digits than letters.								Even
22		J636P1G		6		J636P1		517X2		On average , there are more 7 chars long licenses than 5 or 6 chars.								Even
23		9D1NXP7		7		9D1NXP7		H900I10										Even
24		17FV0T8		7		17FV0T8		9S6463										Odd
25		H28ZT09		5		H28ZT		L12G788										Even
26		31NO3V9		7		31NO3V9		G5U015B										Odd
27		1V23C88		7		1V23C88		745293C										Odd
28		H8B6922		6		H8B692		1890G										Even
29		8EX34Z1		6		8EX34Z		P664K9										Odd
30		8493814		6		849381		06R77AF										Odd
31		09XSFC8		5		09XSF		17NV3T6										Even
32		ST82G4E		7		ST82G4E		53MM493										Odd
33		375DFR7		7		375DFR7		T6HZYK2										Even
34		8E06P95		6		8E06P9		E511Z6V										Even
35		1I570RS		7		1I570RS		VB676R										Even
36		4992Y6D		7		4992Y6D		0023KA										Odd
37		292F6A9		7		292F6A9		5Q5328										Even
38		NF2851S		6		NF2851		52A414										Even
39		77J1524		7		77J1524		24JJI62										Even
40		PE45Z50		7		PE45Z50		62X6D6M										Even
41		9W5NDZ1		7		9W5NDZ1		819Z8										Even
42		848Q145		7		848Q145		5A88LFE										Even
43		6915907		7		6915907		0646957										Odd
44
Lic Plt Gen 3

Cell Formulas
Range	Formula
B7	B7	=FORMULATEXT(B12)
D10	D10	=FORMULATEXT(D12)
F11,R11	F11	=FORMULATEXT(F12)
B12:B43	B12	=LET(n,C4,s,SEQUENCE(66,,65),q,IF(s>90,RIGHT(s,1),CHAR(s)),BYROW(INDEX(q,RANDARRAY(n,7,1,66,1)),LAMBDA(x,TEXTJOIN(,,x))))
D12:D43	D12	=LET(d,RANDARRAY(C4,,5,10,1),IF(d>7,7,d))
F12:F43	F12	=LEFT(B12#,D12#)
H12:H43	H12	=LET(n,C4,s,SEQUENCE(66,,65),q,IF(s>90,RIGHT(s,1),CHAR(s)),b,BYROW(INDEX(q,RANDARRAY(n,7,1,66,1)),LAMBDA(x,TEXTJOIN(,,x))),d,RANDARRAY(n,,5,10,1),LEFT(b,IF(d>7,7,d)))
R12:R43	R12	=MAP(H12#,LAMBDA(x,EO(x)))
Dynamic array formulas.

 

[Xlambda]

Found a trick to improve both solutions of Even/Odd main challenge.
Appending a leading 1 to any number, since only last digit is relevant for an even/odd check, will not affect the outcome result.
Why a 1 ? Because if a string has only letters that will be ignored or replaced with "", this 1 will deliver "Odd", and this is exactly what we need.
If we append "1" as leading char to each license plate nr., recursive EO function does not need IF(n=0,"Odd"….anymore.
Also REDUCE/SUBSTITUTE solution delivers only digits, => no need for an IFERROR check anymore.
New recursive EO function in these circumstances

=LAMBDA(a,
    LET(
        c, 1 & a,
        n, LEN(c),
        x, ISODD(RIGHT(c, 1)),
        IF(ISERR(x), EO(LEFT(c, n - 1)), IF(x, "Odd", "Even"))
    )
)

Excel-Challenge-License-Plates.xlsx
	A	B	C	D	E	F	G	H	I	J	K	L	M
1	License Plate Challenge			Rule: If last digit of license plate is odd nr. than "Odd", else "Even", if no digits found => "Odd"
2	appending 1 trick			2nd solution, entire clm vector, 2 steps only
3		1st solution, new EO		=REDUCE(1&A6:A55,CHAR(SEQUENCE(26,,65)),LAMBDA(v,x,SUBSTITUTE(v,x,"")))
4		=EO([@[Plate Number]])		↓↓↓		=IF(ISODD(+D6#),"Odd","Even")
5	Plate Number	Odd/Even		↓↓↓		↓↓↓
6	123M57	Odd		112357		Odd		Notes:
7	1COU886	Even		11886		Even		- No need to extract right most digit,
8	1D48821	Odd		1148821		Odd		ISODD(whole nr) will return same results
9	1DVT189	Odd		11189		Odd		- since ISODD is a math op, no need for dbl negative
10	21W7454	Even		1217454		Even
11	27U17	Odd		12717		Odd		=VALUETOTEXT(11)		=ISODD(H12)
12	2IGR878	Even		12878		Even		11		TRUE
13	2RDZ434	Even		12434		Even
14	2SWQ185	Odd		12185		Odd		- "+" sign in ISODD(+D6#), only "forces" ISODD to handle arrays
15	3FII697	Odd		13697		Odd
16	3QOW866	Even		13866		Even				=ISODD(H17:H18)		=ISODD(+H17:H18)
17	3RQC229	Odd		13229		Odd		11		#VALUE!		TRUE
18	3RSZ114	Even		13114		Even		122				FALSE
19	4FXL296	Even		14296		Even
20	4KUC981	Odd		14981		Odd
21	4QKB212	Even		14212		Even		check results, both solutions
22	4QRG241	Odd		14241		Odd		=AND(F6#=tblChallenge[Odd/Even])
23	4RVF139	Odd		14139		Odd		TRUE
24	5ACY568	Even		15568		Even
25	5IYF234	Even		15234		Even
26	5KFC128	Even		15128		Even
27	5NFD419	Odd		15419		Odd
28	5RXA984	Even		15984		Even
29	5TGB871	Odd		15871		Odd
30	5UEZ777	Odd		15777		Odd
31	5WKT763	Odd		15763		Odd
32	6LJT722	Even		16722		Even
33	6MVB117	Odd		16117		Odd
34	6XZR265	Odd		16265		Odd
35	71F27UJ	Odd		17127		Odd
36	745Y4I	Even		17454		Even
37	76736Q	Even		176736		Even
38	7FOB933	Odd		17933		Odd
39	7JCM371	Odd		17371		Odd
40	884PCX	Even		1884		Even
41	8JHC777	Odd		18777		Odd
42	8RDQ178	Even		18178		Even
43	8TMW513	Odd		18513		Odd
44	9PMH329	Odd		19329		Odd
45	9UGW414	Even		19414		Even
46	9UUL349	Odd		19349		Odd
47	BEACH	Odd		1		Odd
48	G97C8T	Even		1978		Even
49	H1R226I	Even		11226		Even
50	KL7469C	Odd		17469		Odd
51	RUSS	Odd		1		Odd
52	S94CO	Even		194		Even
53	T5A5MEN	Odd		155		Odd
54	YELOSTN	Odd		1		Odd
55	YOSEMIT	Odd		1		Odd
56
Challenge

Cell Formulas
Range	Formula
D3	D3	=FORMULATEXT(D6)
B4,F4	B4	=FORMULATEXT(B6)
D6:D55	D6	=REDUCE(1&A6:A55,CHAR(SEQUENCE(26,,65)),LAMBDA(v,x,SUBSTITUTE(v,x,"")))
F6:F55	F6	=IF(ISODD(+D6#),"Odd","Even")
H11,J11,H22,J16,L16	H11	=FORMULATEXT(H12)
H12	H12	=VALUETOTEXT(11)
J12	J12	=ISODD(H12)
J17	J17	=ISODD(H17:H18)
L17:L18	L17	=ISODD(+H17:H18)
H23	H23	=AND(F6#=tblChallenge[Odd/Even])
B6:B55	B6	=EO([@[Plate Number]])
Dynamic array formulas.

 

[Xlambda]

3rd solution, and still unconventional (without using MID)

Excel-Challenge-License-Plates.xlsx
	A	B	C	D	E	F	G	H	I	J
1	License Plate Challenge
2
3		3rd solution
4		=IF(ISODD(TEXTJOIN(,,TEXTSPLIT(1&A6,CHAR(SEQUENCE(26,,65))))),"Odd","Even")
5	Plate Number	Odd/Even
6	123M57	Odd
7	1COU886	Even		If strings with lowercase values, we can use UPPER
8	1D48821	Odd
9	1DVT189	Odd		=IF(ISODD(TEXTJOIN(,,TEXTSPLIT(1&UPPER(D11),CHAR(SEQUENCE(26,,65))))),"Odd","Even")
10	21W7454	Even				↓↓↓
11	27U17	Odd		zA		Odd
12	2IGR878	Even		xa34d		Even
13	2RDZ434	Even		DsTr		Odd
14	2SWQ185	Odd		z357wP300fG		Even
15	3FII697	Odd		2uyfoTYFIIYTF		Even
16	3QOW866	Even		2VnM2223lLkJH		Odd
17	3RQC229	Odd
18	3RSZ114	Even
19	4FXL296	Even
20	4KUC981	Odd
21	4QKB212	Even
22	4QRG241	Odd
23	4RVF139	Odd
24	5ACY568	Even
25	5IYF234	Even
26	5KFC128	Even
27	5NFD419	Odd
28	5RXA984	Even
29	5TGB871	Odd
30	5UEZ777	Odd
31	5WKT763	Odd
32	6LJT722	Even
33	6MVB117	Odd
34	6XZR265	Odd
35	71F27UJ	Odd
36	745Y4I	Even
37	76736Q	Even
38	7FOB933	Odd
39	7JCM371	Odd
40	884PCX	Even
41	8JHC777	Odd
42	8RDQ178	Even
43	8TMW513	Odd
44	9PMH329	Odd
45	9UGW414	Even
46	9UUL349	Odd
47	BEACH	Odd
48	G97C8T	Even
49	H1R226I	Even
50	KL7469C	Odd
51	RUSS	Odd
52	S94CO	Even
53	T5A5MEN	Odd
54	YELOSTN	Odd
55	YOSEMIT	Odd
56
Challenge

Cell Formulas
Range	Formula
B4	B4	=FORMULATEXT(B6)
D9	D9	=FORMULATEXT(F11)
F11:F16	F11	=IF(ISODD(TEXTJOIN(,,TEXTSPLIT(1&UPPER(D11),CHAR(SEQUENCE(26,,65))))),"Odd","Even")
B6:B55	B6	=IF(ISODD(TEXTJOIN(,,TEXTSPLIT(1&A6,CHAR(SEQUENCE(26,,65))))),"Odd","Even")