Declare @fgr table (
	id int,
	fgr int
)

Declare @t table (
	id int identity(1,1),
	st int,
	gr varchar(100)
)

Insert Into @t
Select top 300
	st = number%50+1,
	gr=''
From master..spt_values
Where number >0
Order By newid()

Declare @rowCount int
set @rowCount = 1

while exists(Select * From @t Where gr = '')
Begin
	while (@rowCount > 0)
	Begin
		Update A
		Set
			gr = convert(varchar,grstr%3+1)+A.gr
		From @t A
		Inner Join
			(
			Select
				id,
				st,
				grstr = Row_Number() Over(Partition By gr, st Order By NewId()),
				grstm = (count(*) Over(Partition By gr, st)/3)*3
			From @t Z
			Where gr not like 'f%'
			and 3 < (Select count(*) From @t Where gr = Z.gr)
			) B
		On A.id = B.id
		Where gr not like 'f%'
		and B.grstr <= grstm

		Set @rowCount= @@RowCount
	End

	if not exists(Select * From @t Where gr not like 'f%' and gr <> '')
	Begin
		if (9 > (Select count(*) From @t Where gr not like 'f%'))
		Begin
			Update A 
			Set gr = 1
			From @t A
			Where gr not like 'f%'
		End
		Else
		Begin
			Update A
			Set 
				gr = B.gr
			From @t A
			Inner Join
				(
				Select 
					id,
					st,
					gr = convert(varchar,Row_Number() Over(Order By st, newid())%3+1)
				From @t Where gr not like 'f%'
				) B
			On A.id = B.id
		End
	End

	Insert Into @fgr
	Select 
		id,
		fgr = Dense_Rank() Over(Order By case when gr like 'f%' then 0 else 1 end, gr, gr2)
	From
		(
		Select
			*,
			gr2 = (grstr-1)/3*3
		From
			(
			Select 
				id,
				st,
				gr,
				grstr = Row_Number() Over(Partition By gr Order By NewId()),
				grstm = (count(*) Over(Partition By gr)/3)*3
			From @t 
			where gr <> ''
			) A
		Where grstr <= grstm
		) Z


	Update A
	Set
		gr = isnull('f'+right(replicate('0',5)+convert(varchar,fgr),5),'')
	From @t A
	Left Join @fgr B
	On A.id = B.id
	Where A.gr not like 'f%'


	--Select * From @t Order By gr
End

Select gr, count(*) From @t Group By gr Order By gr

Select 
	id1 = B.id,
	st1 = B.st,
	id2 = A.id,
	st2 = A.st,
	id3 = C.id,
	st3 = C.st,
	StateCondition = Case when A.st = B.st or A.st = C.st or B.st = C.st then 'Fail' else '' end
From @t A
Inner Join @t B
On A.gr = B.gr
and A.id > B.id
Inner Join @t C
On A.gr = C.gr
and A.id < C.id

Declare @t table (
	id int identity(1,1),
	st int,
	gr int
)

Insert Into @t
Select top 300
	st = number%50+1,
	gr=null
From master..spt_values
Where number>0 and number<=1000
Order By newid()

Declare @grpSize int,
	@grpCount int

Set @grpSize = 3
Set @grpCount = (Select count(*) From @t)/@grpSize


Update A
Set
	gr = B.gr
From @t A
Inner Join
	(
	Select 
		Z.id,
		Z.st, 
		gr = Row_Number()Over(Order By Y.o, newid())%@grpCount+1
	From @t Z
	Inner Join 
		(
		Select 
			st, 
			o = Row_Number()Over(Order By count(*) Desc, newid())
		From @t
		Group By st
		) Y
	On Z.st = Y.st
	) B
On A.id = B.id
	
	Select 
		A.gr,
		id1 = B.id,
		st1 = B.st,
		id2 = A.id,
		st2 = A.st,
		id3 = C.id,
		st3 = C.st,
		StateCondition = Case when A.st = B.st or A.st = C.st or B.st = C.st then 'Fail' else '' end
	From @t A
	Inner Join @t B
	On A.gr = B.gr
	and A.id > B.id
	Inner Join @t C
	On A.gr = C.gr
	and A.id < C.id
	Where A.gr <> ''
	Order By 8 Desc, 1

a) Group 1 - State 1 - State 2 - State 3
   Group 2 - State 6 - State 5 - State 9

b) Group 1 - State 1
   Group 1 - State 2
   Group 1 - State 3
   Group 2 - State 6
   Group 2 - State 5
   Group 2 - State 9

SET NOCOUNT ON

-- Create sample data
CREATE TABLE	#Pool
		(
			PlayerID INT IDENTITY(1, 1) PRIMARY KEY,
			StateCode TINYINT NOT NULL,
			GroupNumber TINYINT
		)

-- Populate sample data
INSERT	#Pool
	(
		StateCode
	)
SELECT	1 + ABS(CHECKSUM(NEWID())) % 50 AS StateCode
FROM	master..spt_values
WHERE	type = 'p'
	AND number BETWEEN 1 AND 300

CREATE NONCLUSTERED INDEX IX_Pool ON #Pool (StateCode) INCLUDE (GroupNumber)

/*
	Solution starts here
*/
-- Mimic user supplied parameter
DECLARE	@GroupSize TINYINT = 3

-- Declare working variables
DECLARE	@WantedGroups TINYINT,
	@CurrCode TINYINT = (SELECT MIN(StateCode) FROM #Pool)

;WITH cteWantedGroups
AS (
	SELECT	NTILE(@GroupSize) OVER (ORDER BY PlayerID) AS SeqID
	FROM	#Pool
)
SELECT TOP(1)	@WantedGroups = COUNT(*)
FROM		cteWantedGroups
GROUP BY	SeqID
ORDER BY	COUNT(*) DESC

CREATE TABLE	#Hat
		(
			SeqID INT IDENTITY(1, 1) PRIMARY KEY,
			Number TINYINT NOT NULL
		)

WHILE EXISTS (SELECT * FROM #Pool WHERE GroupNumber IS NULL)
	BEGIN
		TRUNCATE TABLE	#Hat

		INSERT		#Hat
				(
					Number
				)
		SELECT		Number
		FROM		(
					SELECT	Number
					FROM	master..spt_values
					WHERE	Type = 'P'
						AND Number BETWEEN 1 AND @WantedGroups

					EXCEPT

					SELECT		GroupNumber
					FROM		#Pool
					WHERE		GroupNumber IS NOT NULL
					GROUP BY	GroupNumber
					HAVING		COUNT(*) = @GroupSize
				) AS d
		ORDER BY	NEWID()

		UPDATE		p
		SET		p.GroupNumber = h.Number
		FROM		(
					SELECT	GroupNumber,
						ROW_NUMBER() OVER (ORDER BY PlayerID) AS SeqID
					FROM	#Pool
					WHERE	StateCode = @CurrCode
						AND GroupNumber IS NULL
				) AS p
		INNER JOIN	#Hat AS h ON h.SeqID = p.SeqID

		SELECT	@CurrCode = MIN(StateCode)
		FROM	#Pool
		WHERE	GroupNumber IS NULL
	END

SELECT		*
FROM		#Pool
ORDER BY	GroupNumber

DROP TABLE	#Pool,
		#Hat

SELECT	DISTINCT 1 + ABS(CHECKSUM(NEWID())) % 50 AS StateCode
FROM	master..spt_values
WHERE	type = 'p'
	AND number BETWEEN 1 AND 300

CREATE UNIQUE NONCLUSTERED INDEX IX_Pool ON #Pool (StateCode) INCLUDE (GroupNumber)