3x3

Question 1

Answer 1

F (R U R’ U’) F’

Question 2

Answer 2

F (R U R’ U’) (R U R’ U’) F

Question 3

Answer 3

F (R U R’ U’) (R U R’ U’) (R U R’ U’) F’
y (R’ U’ R) U’ (R’ U R) U’ (R’ U2 R)

Question 4

Question 5

Question 6

Answer 6

f ‘ (L’ U’ L U) f

Question 7

Answer 7

F’ (L’ U’ L U) (L’ U’ L U) F

Question 8

Answer 8

[F (R U R’ U’) F’] U [F (R U R’ U’) F’]

Question 9

Answer 9

[F’ (L’ U’ L U) F] y [F (R U R’ U’) F’]
y (r U R’ U)(R’ F R F’) R U2 r’

Question 10

Answer 10

[f (R U R’ U’) f’] U [F (R U R’ U’) F’]

Question 11

Answer 11

[f (R U R’ U’) f’] U’ [F (R U R’ U’) F’]

Question 12

Answer 12

[F (R U R’ U’) F’] [f (R U R’ U’) f’]

Question 13

Question 14

Answer 14

(r U r’) (R U R’ U’) (r U’ r’)

Question 15

Answer 15

(l’ U’ l) (L’ U’ L U) (l’ U l)

Question 16

Question 17

Answer 17

(R U R’ U’) M’ (U R U’ r’)

Question 18

Answer 18

M U (R U R’ U’) M2 (U R U’ r’)

Question 19

Question 20

Answer 20

(R U R’ U’) (R’ F R F’)

Question 21

Question 22

Answer 22

F’ (r U R’ U’) (r’ F R )

Question 23

Answer 23

R’ U’ (R’ F R F’) U R

Question 24

Answer 24

R U2 R’) (R’ F R F’) U2 (R’ F R F’)

Question 25

Answer 25

(R U2 R’) (R’ F R F’) (R U2 R’)

Question 26

Answer 26

M U (R U R’ U’) M’ (R’ F R F’)

Question 27

Answer 27

(R’ F R’ F’) R2 U2 y (R’ F R F’)

Question 28

Answer 28

(R U R’ U) (R U’ R’ U’) (R’ F R F’)

Question 29

Answer 29

(L’ U’ L U’) (L’ U L U) (L F’ L’ F)

Question 30

Answer 30

(R U R’ U) R d’ R U’ R’ F’
(R’ U’ R U’) R’ d R’ U R B

Question 31

Answer 31

(R U R’ U) (R’ F R F’) U2 (R’ F R F’)

Question 32

Answer 32

[F (R U R’ U) F’] y’ U2 (R’ F R F’)

Question 33

Question 34

Answer 34

(r U R’ U) R U2 r’

Question 35

Answer 35

(R U R’ U) R U2 R’

Question 36

Question 37

Answer 37

[R’ U2 (R U R’ U) R] y [F (R U R’ U’) F’]

(R’ F R F’) (R’ F R F’) (R U R’ U’) (R U R’)

Question 38

Answer 38

[(R U R’ U) R U2 R’] [F (R U R’ U’) F’]

Question 39

Answer 39

(r U R’ U) (R U’ R’ U) R U2’ r

Question 40

Answer 40

l’ U’ L U’ L’ U L U’ L’ U2 l
y2 r’ U’ R U’ R’ U R U’ R’ U2 r

Question 41

Answer 41

r U2 R’ U’ R U’ r’

Question 42

Answer 42

F R U’ R’ U’ R U R’ F’

Question 43

Answer 43

r’ U’ R U’ R’ U2 r

Question 44

Answer 44

M’ U M U2 M’ U M

Question 45

Answer 45

(R U R2 U’) (R’ F) (R U) (R U’) F’
(R U R’ U’) x D’ R’ U R U’ D x’

Question 46

Answer 46

F U R U’ R2 F’ R (U R U’ R’)

Question 47

Question 48

Answer 48

R2 [D (R’ U2) R] [D’ (R’ U2) R’]

Question 49

Answer 49

R’ U2 R2 U R’ U R U2 x’ U’ R’ U

Question 50

Answer 50

R U B’ U’ R’ U R B R’
R d L’ d’ R’ U R B R’

Question 51

Answer 51

R’ U’ F U R U’ R’ F’ R
y2 L’ d’ R d L U’ L’ B’ L

Question 52

Answer 52

R B’ R’ U’ R U B U’ R’
y2 L F’ (L’ U’ L U) F U’ L’

Question 53

Answer 53

R’ F R2 B’ R2’ F’ R2 B R’

Question 54

Answer 54

R U R’ U’) R U’ R’ F’ U’ F (R U R’)
[F (R U R’ U’) F’] U2 [(R U R’ U’) (R’ F R F’)]

Question 55

Answer 55

(R2 U R’ B’ R) U’ (R2 U R B R’)

Question 56

Answer 56

(R’ U’ R) y’ x’ (R U’) (R’ F) (R U R’)
(R U R’ U’) R’ F R2 U R’ U’ F’

Question 57

Answer 57

R U R’ y R’ F R U’ R’ F’ R
(R U R’ U) (R’ F R F’) R U2 R’