15 balls sorting tracking tuples and candidates

Sort 15 into Tuples of Three:						5
ABC, DEF, GHI, JKL, MNO (sorted light to heavy)
Candidates for 15 (heaviest):			CFILO
Candidates for 14:			BCEFHIKLNO
Candidates for 2:			ABDEGHJKMN
Candidates for 1:			ADGJM
Found: 			none

Sort CFI to PQR:						6
AB, DE, GH, JKL, MNO, PQR
Candidates for 15 (heaviest):			LOR
Candidates for 14:			BEHKLNOQR
Candidates for 2:			ABDEGHJKMN
Candidates for 1:			ADGJM
Found: 			none

Sort LOR to STU:						7
AB, DE, GH, JK, MN, PQ, STU
Candidates for 15 (heaviest):			U
Candidates for 14:			BEHKNQT
Candidates for 13:			AB, DE, GH, JK, MN, PQ, ST
Candidates for 2:			ABDEGHJKMN
Candidates for 1:			ADGJM
Found:			15

Sort ADG to VWX:						8
B, E, H, JK, MN, PQ, ST, VWX
Candidates for 14:			BEHKNQT
Candidates for 13:			B, E, H, JK, MN, PQ, ST, WX
Candidates for 2:			BEHJKMNVW
Candidates for 1:			JMV
Found:			15

Sort JMV to YZα:						9
B, E, H, K, N, PQ, STU, WX, YZα
Candidates for 14:			BEHKNQT
Candidates for 13:			B, E, H, K, N, PQ, ST, WX Zα
Candidates for 3:			B, E, H, K, N, PQ, ST, WX, Zα
Candidates for 2:			BEHKNWZ
Candidates for 1:			Y
Found:			1,15

Sort BEH to βγδ:						10
K, N, PQ, ST, WX, Zα, βγδ
Candidates for 14:			KNQTδ
Candidates for 13:			K, N, PQ, ST, WX Zα γδ
Candidates for 3:			K, N, PQ, ST, WX, Zα βγ
Candidates for 2:			KNWZβ
Found:			1,15

Sort KNQ to εζη:						11
P, ST, WX, Zα, βγδ, εζη
Candidates for 14:			Tδη
Candidates for 13:			P, ST, WX Zα γδ ζη
Candidates for 3:			P, ST, WX, Zα βγ εζ
Candidates for 2:			WZβε
Found:			1,15

Sort Tδη to θικ:						12
P, S, WX, Zα, βγ, εζ, θικ
Candidates for 14:			κ
Candidates for 13:			P, S, WX Zα γ ζ ι
Candidates for 12:			P, S, WX, Zα, βγ, εζ, θι
Candidates for 3:			P, S, WX, Zα βγ εζ
Candidates for 2:			WZβε
Found:			1, 14, 15

Sort WZβ to λμν:						13
P, S, X, α, γ, εζ, θι, λμν
Candidates for 13:			P, S, X α γ ζ θι ν
Candidates for 12:			P, S, X, α, γ, εζ, ι μν
Candidates for 3:			P, S, X, α γ εζ λμ
Candidates for 2:			ελ
Found:			1, 14, 15

Sort Pελ to ξπρ:						14
S, X, α, γ, ζ, θι, μν, ξπρ
Candidates for 13:			S, X α γ ζ ι ν ρ
Candidates for 12:			S, X, α, γ, ζ, θι μν πρ
Candidates for 4:			S, X, α, γ, ζ, θ, μν, πρ
Candidates for 3:			S, X, α γ ζ μ, π
Candidates for 2:			ξ
Found:			1, 2, 14, 15

Sort SXα to στυ:						15
 γ, ζ, θι, μν, πρ, στυ
Candidates for 13:			γ ζ ι ν ρ υ
Candidates for 12:			γ, ζ, θι μν πρ τυ
Candidates for 4:			γ, ζ, θ, μν, πρ στ
Candidates for 3:			γ ζ μ π σ
Found:			1, 2, 14, 15

Sort γζι to φχψ:						16
θ, μν, πρ, στυ, φχψ
Candidates for 13:			ν ρ υ ψ
Candidates for 12:			θ μν πρ τυ χψ
Candidates for 4:			θ, μν, πρ στ φχ
Candidates for 3:			μ, π σ φ
Found:			1, 2, 14, 15

Sort νρυ to ωAB:						17
θ, μ, π, στ, φχψ, ωAB
Candidates for 13:			ψ B
Candidates for 12:			θ μ π τ χψ AB
Candidates for 4:			θ, μ, π στ φχ ωA
Candidates for 3:			μ, π σ φ
Found:			1, 2, 14, 15

Sort θψB to CDE:						18
μ, π, στ, φχ, ωA, CDE
Candidates for 13:			E
Candidates for 12:			μ π τ χ A D
Candidates for 11:			μ, π, στ, φχ, ωA, CD
Candidates for 4:			μ, π στ φχ ωA C
Candidates for 3:			μ, π σ φ
Found:			1, 2, 13, 14, 15

Sort μπσ to FGH:						19
τ, φχ, ωA, CD, FGH
Candidates for 12:			τ χ A D H
Candidates for 11:			τ, φχ, ωA, CD GH
Candidates for 4:			τ φχ ωA C FG
Candidates for 3:			φ F
Found:			1, 2, 13, 14, 15

Sort τφF to IJK:						20
χ, ωA, CD, GH, IJK
Candidates for 12:			χ A D H K
Candidates for 11:			χ, ωA, CD GH JK
Candidates for 5:			χ, ωA, CD, GH, JK
Candidates for 4:			χ ωA C G J
Candidates for 3:			I
Found:			1, 2, 3, 13, 14, 15

Sort χAD to LMN:						21
ω, C, GH, JK, LMN
Candidates for 12:			H K N
Candidates for 11:			ω, C GH JK MN
Candidates for 5:			ω, C, GH, JK LM
Candidates for 4:			ω C G J L
Found:			1, 2, 3, 13, 14, 15

Sort HKN to OPQ:						22
ω, C, G, J, LM, OPQ
Candidates for 12:			Q
Candidates for 11:			ω, C G J M P
Candidates for 10:			ω, C, G, J, LM OP
Candidates for 5:			ω, C, G, J LM O
Candidates for 4:			ω C G J L
Found:			1, 2, 3, 12, 13, 14, 15

Sort ωCG to RST:						23
J, LM, OP, RST
Candidates for 11:			J M P T
Candidates for 10:			J, LM OP ST
Candidates for 5:			J LM O RS
Candidates for 4:			J L R
Found:			1, 2, 3, 12, 13, 14, 15

Sort JLR to UVW:						24
M, OP, ST, UVW
Candidates for 11:			M P T W
Candidates for 10:			M OP ST VW
Candidates for 6:			M, OP, ST, VW
Candidates for 5:			M O S V
Candidates for 4:			U
Found:			1, 2, 3, 4, 12, 13, 14, 15

Sort MPT to XYZ:						25
O, S, VW, XYZ
Candidates for 11:			W Z
Candidates for 10:			O S VW YZ
Candidates for 6:			O, S, VW XY
Candidates for 5:			O S V X
Found:			1, 2, 3, 4, 12, 13, 14, 15

Sort OWZ to αβγ:						26
S, V, XY, αβγ
Candidates for 11:			γ
Candidates for 10:			S V Y β
Candidates for 9:			S, V, XY, αβ
Candidates for 6:			S, V XY αβ
Candidates for 5:			S V X α
Found:			1, 2, 3, 4, 11, 12, 13, 14, 15

Sort SVX to δεζ:						27
Y, αβ, δεζ
Candidates for 10:			Y β ζ
Candidates for 9:			Y, αβ εζ
Candidates for 6:			Y αβ δε
Candidates for 5:			α δ
Found:			1, 2, 3, 4, 11, 12, 13, 14, 15

Sort Yαδ to ηθι:						28
β, εζ, ηθι
Candidates for 10:			β ζ ι
Candidates for 9:			β εζ θι
Candidates for 7:			β, εζ, θι
Candidates for 6:			β ε θ
Candidates for 5:			η
Found:			1, 2, 3, 4, 5, 11, 12, 13, 14, 15

Sort βζι to κλμ:						29
ε, θ, κλμ
Candidates for 10:			μ
Candidates for 9:			ε θ λμ
Candidates for 8:			ε, θ, κλ
Candidates for 7:			ε, θ κλ
Candidates for 6:			ε θ κ
Found:			1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15

Sort εθκ to νξπ:						30
λ, ξπ
Candidates for 9:			λ π
Candidates for 8:			λ ξπ
Candidates for 7:			λ ξ
Candidates for 6:			ν
Found:			1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 15

Sort λξπ to ρστ:						31
Candidates for 9:			τ
Candidates for 8:			σ
Candidates for 7:			ρ
Found:			1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15