DEVIL'S ALGORITHM FOR RUBIK'S 3x3 CUBE
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First, define the following algorithms:
(COC1) = F D2 F' R' D2 R U R' D2 R F D2 F' U'
(COC2) = F (COC1) F'
(COC3) = L F (COC1) F' L'
(COC4) = F' (COC1) F
(COC5) = F2 (COC1) F2
(COC6) = L' F2 (COC1) F2 L
(COC7) = D' F' (COC1) F D
(EOC1) = L R' F L R' D L R' B2 L' R D L' R F L' R U2
(EOC2) = L F (EOC1) F' L'
(EOC3) = R' F' (EOC1) F R
(EOC4) = F (EOC1) F'
(EOC5) = F' (EOC1) F
(EOC6) = U L U' (EOC1) U L' U'
(EOC7) = U' R' U (EOC1) U' R U
(EOC8) = F2 (EOC1) F2
(EOC9) = D (EOC8) D'
(EOC10) = D' (EOC8) D
(EOC11) = D2 (EOC8) D2
(EPC2) = U F2 U F2 D' L2 B2 U' B2 D L2 F2 D2 B2 D2 F2
(EPC3) = U' D L2 U D' B2
(EPC4) = U F2 U F2 D' L2 B2 D' R2 U R2 F2 D2 B2 U2 B2
(EPC5) = B L' B U2 D2 F' R F' U2 D2
(EPC6) = L D' F2 U' B2 U' R U2 R' F2 R2 F2 D' R2 D F2 D
(EPC7) = B2 U R B2 D2 B2 R B2 U' D' L2 D' B2
(EPC8) = B2 L F' U' B2 U F L' R2 B2 U' D2 L2 D' B2 U
(EPC9) = B2 R B2 D2 B2 R B2 U' L2 U D' F2 U' F2 B2
(EPC10) = D2 R' F U B2 U' F' R U2 B2 D' F2 R2 U F2 U F2
(EPC11) = B2 R2 U' L' D2 B2 U2 R' U2 R2 F2 L2 R2 U R2
(EPC12) = D2 L' B2 U2 F2 R U L2 U' F2 R2 U' R2 U2 F2 D L2 D'
(CPC2) = U B2 U' L2 D L2 B2 D B2 D' B2
(CPC3) = B R' B L2 B' R B L2 B2
(CPC4) = U F2 B2 U' F2 B2 U' F2 L2 R2 B2 R2
(CPC5) = R2 U' F2 D R2 U F2 D' R2 D F2 R2 D' F2
(CPC6) = U' F2 D F2 U L2 F2 D L2 D F2 L2 D2 F2
(CPC7) = U2 D' L2 U' F2 L2 U' B2 L2 R2 U' L2 B2
(CPC8) = F2 D' R2 U2 L2 B2 U F2 L2 U2 F2 L2 U F2 R2
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Then "build" the Devil's algorithm by using the above definitions like this. Note how each new algorithm uses the previous one in some way.
(COT1) = (COC1)3
(COT2) = [(COC2)(COT1)]3
(COT3) = [(COC3)(COT2)]3
(COT4) = [(COC4)(COT3)]3
(COT5) = [(COC5)(COT4)]3
(COT6) = [(COC6)(COT5)]3
(CO) = (COT7) = [(COC7)(COT6)]3 (48,600 moves)
(EOT1) = [(EOC1)(CO)]2
(EOT2) = [(EOC2)(EOT1)]2
(EOT3) = [(EOC3)(EOT2)]2
(EOT4) = [(EOC4)(EOT3)]2
(EOT5) = [(EOC5)(EOT4)]2
(EOT6) = [(EOC6)(EOT5)]2
(EOT7) = [(EOC7)(EOT6)]2
(EOT8) = [(EOC8)(EOT7)]2
(EOT9) = [(EOC9)(EOT8)]2
(EOT1O) = [(EOC10)(EOT9)]2
(O) = (EO) = (EOT11) = [(EOC11)(EOT1O)]2 (199,228,148 moves)
(EPT2) = [(EPC2)(O)]2
(EPT3) = [(EPC3)(EPT2)]3
(EPT4) = [(EPC4)(EPT3)]4
(EPT5) = [(EPC5)(EPT4)]5
(EPT6) = [(EPC6)(EPT5)]6
(EPT7) = [(EPC7)(EPT6)]7
(EPT8) = [(EPC8)(EPT7)]8
(EPT9) = [(EPC9)(EPT8)]9
(EPT10) = [(EPC10)(EPT9)]10
(EPT11) = [(EPC11)(EPT10)]11
(EP) = (EPT12) = [(EPC12)(EPT11)]12 (95,430,612,313,219,476 moves)
(CPT2) = [(CPC2)(EP)]2
(CPT3) = [(CPC3)(CPT2)]3
(CPT4) = [(CPC4)(CPT3)]4
(CPT5) = [(CPC5)(CPT4)]5
(CPT6) = [(CPC6)(CPT5)]6
(CPT7) = [(CPC7)(CPT6)]7
(D) = (CP) = (CPT8) = [(CPC8)(CPT7)]8 (3,847,762,288,469,010,006,992 moves)
(D) is Devil's Algorithm. If you apply it to the cube, it will be solved at some point before you have done the algorithm once. As you can see, it is terribly long, nearly a thousand times more moves than there are possible positions.