Master Circular Mixed Facing - Intermediate-Advanced Level Problems Circular Mixed Facing INTERMEDIATE ADVANCED

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix N (faces center) at position 1 (reference point)
- Q faces outward, sits third to the RIGHT of N:
N faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- O sits second to the LEFT of N (pos 1):
N faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
O faces same as Q → OUTWARD
- M faces center, sits immediately to the RIGHT of O (pos 7):
O faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- P immediately to the RIGHT of N(pos 1, center→CW): pos 2
- R opposite N(pos 1): pos 5
- S not adjacent to Q(pos 4): adj = pos 3 & 5
→ S at pos 8, T at pos 3

Final Arrangement (clockwise):
pos1:N(ctr) | pos2:P(out) | pos3:T(ctr) | pos4:Q(out) | pos5:R(out) | pos6:M(ctr) | pos7:O(out) | pos8:S(ctr)

Find second to the right of M (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = S

Verification:
✓ Q(outward) 3 left of N(center): 3 ACW from pos1 = pos4
✓ O 2nd left of N, same direction as Q (outward)
✓ M(center) immediately right of O(outward, right=ACW)
✓ P immediately right (CW) of N
✓ R opposite N
✓ S not adjacent to Q

Answer: S sits second to the right of M.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix N (faces center) at position 1 (reference point)
- O faces outward, sits third to the RIGHT of N:
N faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- P sits second to the LEFT of N (pos 1):
N faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
P faces same as O → OUTWARD
- T faces center, sits immediately to the RIGHT of P (pos 7):
P faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- R immediately to the RIGHT of N(pos 1, center→CW): pos 2
- Q opposite N(pos 1): pos 5
- M not adjacent to O(pos 4): adj = pos 3 & 5
→ M at pos 8, S at pos 3

Final Arrangement (clockwise):
pos1:N(ctr) | pos2:R(out) | pos3:S(ctr) | pos4:O(out) | pos5:Q(out) | pos6:T(ctr) | pos7:P(out) | pos8:M(ctr)

Find second to the right of T (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = M

Verification:
✓ O(outward) 3 left of N(center): 3 ACW from pos1 = pos4
✓ P 2nd left of N, same direction as O (outward)
✓ T(center) immediately right of P(outward, right=ACW)
✓ R immediately right (CW) of N
✓ Q opposite N
✓ M not adjacent to O

Answer: M sits second to the right of T.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix M (faces center) at position 1 (reference point)
- R faces outward, sits third to the RIGHT of M:
M faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- N sits second to the LEFT of M (pos 1):
M faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
N faces same as R → OUTWARD
- S faces center, sits immediately to the RIGHT of N (pos 7):
N faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- P immediately to the RIGHT of M(pos 1, center→CW): pos 2
- Q opposite M(pos 1): pos 5
- T not adjacent to R(pos 4): adj = pos 3 & 5
→ T at pos 8, O at pos 3

Final Arrangement (clockwise):
pos1:M(ctr) | pos2:P(out) | pos3:O(ctr) | pos4:R(out) | pos5:Q(out) | pos6:S(ctr) | pos7:N(out) | pos8:T(ctr)

Find second to the right of S (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = T

Verification:
✓ R(outward) 3 left of M(center): 3 ACW from pos1 = pos4
✓ N 2nd left of M, same direction as R (outward)
✓ S(center) immediately right of N(outward, right=ACW)
✓ P immediately right (CW) of M
✓ Q opposite M
✓ T not adjacent to R

Answer: T sits second to the right of S.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix N (faces center) at position 1 (reference point)
- S faces outward, sits third to the RIGHT of N:
N faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- Q sits second to the LEFT of N (pos 1):
N faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
Q faces same as S → OUTWARD
- M faces center, sits immediately to the RIGHT of Q (pos 7):
Q faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- R immediately to the RIGHT of N(pos 1, center→CW): pos 2
- O opposite N(pos 1): pos 5
- T not adjacent to S(pos 4): adj = pos 3 & 5
→ T at pos 8, P at pos 3

Final Arrangement (clockwise):
pos1:N(ctr) | pos2:R(out) | pos3:P(ctr) | pos4:S(out) | pos5:O(out) | pos6:M(ctr) | pos7:Q(out) | pos8:T(ctr)

Find second to the right of M (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = T

Verification:
✓ S(outward) 3 left of N(center): 3 ACW from pos1 = pos4
✓ Q 2nd left of N, same direction as S (outward)
✓ M(center) immediately right of Q(outward, right=ACW)
✓ R immediately right (CW) of N
✓ O opposite N
✓ T not adjacent to S

Answer: T sits second to the right of M.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix M (faces center) at position 1 (reference point)
- N faces outward, sits third to the RIGHT of M:
M faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- R sits second to the LEFT of M (pos 1):
M faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
R faces same as N → OUTWARD
- O faces center, sits immediately to the RIGHT of R (pos 7):
R faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- Q immediately to the RIGHT of M(pos 1, center→CW): pos 2
- P opposite M(pos 1): pos 5
- T not adjacent to N(pos 4): adj = pos 3 & 5
→ T at pos 8, S at pos 3

Final Arrangement (clockwise):
pos1:M(ctr) | pos2:Q(out) | pos3:S(ctr) | pos4:N(out) | pos5:P(out) | pos6:O(ctr) | pos7:R(out) | pos8:T(ctr)

Find second to the right of O (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = T

Verification:
✓ N(outward) 3 left of M(center): 3 ACW from pos1 = pos4
✓ R 2nd left of M, same direction as N (outward)
✓ O(center) immediately right of R(outward, right=ACW)
✓ Q immediately right (CW) of M
✓ P opposite M
✓ T not adjacent to N

Answer: T sits second to the right of O.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix Q (faces center) at position 1 (reference point)
- S faces outward, sits third to the RIGHT of Q:
Q faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- R sits second to the LEFT of Q (pos 1):
Q faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
R faces same as S → OUTWARD
- N faces center, sits immediately to the RIGHT of R (pos 7):
R faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- T immediately to the RIGHT of Q(pos 1, center→CW): pos 2
- P opposite Q(pos 1): pos 5
- O not adjacent to S(pos 4): adj = pos 3 & 5
→ O at pos 8, M at pos 3

Final Arrangement (clockwise):
pos1:Q(ctr) | pos2:T(out) | pos3:M(ctr) | pos4:S(out) | pos5:P(out) | pos6:N(ctr) | pos7:R(out) | pos8:O(ctr)

Find second to the right of N (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = O

Verification:
✓ S(outward) 3 left of Q(center): 3 ACW from pos1 = pos4
✓ R 2nd left of Q, same direction as S (outward)
✓ N(center) immediately right of R(outward, right=ACW)
✓ T immediately right (CW) of Q
✓ P opposite Q
✓ O not adjacent to S

Answer: O sits second to the right of N.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix Q (faces center) at position 1 (reference point)
- S faces outward, sits third to the RIGHT of Q:
Q faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- N sits second to the LEFT of Q (pos 1):
Q faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
N faces same as S → OUTWARD
- P faces center, sits immediately to the RIGHT of N (pos 7):
N faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- T immediately to the RIGHT of Q(pos 1, center→CW): pos 2
- R opposite Q(pos 1): pos 5
- O not adjacent to S(pos 4): adj = pos 3 & 5
→ O at pos 8, M at pos 3

Final Arrangement (clockwise):
pos1:Q(ctr) | pos2:T(out) | pos3:M(ctr) | pos4:S(out) | pos5:R(out) | pos6:P(ctr) | pos7:N(out) | pos8:O(ctr)

Find second to the right of P (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = O

Verification:
✓ S(outward) 3 left of Q(center): 3 ACW from pos1 = pos4
✓ N 2nd left of Q, same direction as S (outward)
✓ P(center) immediately right of N(outward, right=ACW)
✓ T immediately right (CW) of Q
✓ R opposite Q
✓ O not adjacent to S

Answer: O sits second to the right of P.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix N (faces center) at position 1 (reference point)
- R faces outward, sits third to the RIGHT of N:
N faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- O sits second to the LEFT of N (pos 1):
N faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
O faces same as R → OUTWARD
- T faces center, sits immediately to the RIGHT of O (pos 7):
O faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- M immediately to the RIGHT of N(pos 1, center→CW): pos 2
- S opposite N(pos 1): pos 5
- Q not adjacent to R(pos 4): adj = pos 3 & 5
→ Q at pos 8, P at pos 3

Final Arrangement (clockwise):
pos1:N(ctr) | pos2:M(out) | pos3:P(ctr) | pos4:R(out) | pos5:S(out) | pos6:T(ctr) | pos7:O(out) | pos8:Q(ctr)

Find second to the right of T (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = Q

Verification:
✓ R(outward) 3 left of N(center): 3 ACW from pos1 = pos4
✓ O 2nd left of N, same direction as R (outward)
✓ T(center) immediately right of O(outward, right=ACW)
✓ M immediately right (CW) of N
✓ S opposite N
✓ Q not adjacent to R

Answer: Q sits second to the right of T.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix R (faces center) at position 1 (reference point)
- N faces outward, sits third to the RIGHT of R:
R faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- S sits second to the LEFT of R (pos 1):
R faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
S faces same as N → OUTWARD
- Q faces center, sits immediately to the RIGHT of S (pos 7):
S faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- T immediately to the RIGHT of R(pos 1, center→CW): pos 2
- M opposite R(pos 1): pos 5
- O not adjacent to N(pos 4): adj = pos 3 & 5
→ O at pos 8, P at pos 3

Final Arrangement (clockwise):
pos1:R(ctr) | pos2:T(out) | pos3:P(ctr) | pos4:N(out) | pos5:M(out) | pos6:Q(ctr) | pos7:S(out) | pos8:O(ctr)

Find second to the right of Q (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = O

Verification:
✓ N(outward) 3 left of R(center): 3 ACW from pos1 = pos4
✓ S 2nd left of R, same direction as N (outward)
✓ Q(center) immediately right of S(outward, right=ACW)
✓ T immediately right (CW) of R
✓ M opposite R
✓ O not adjacent to N

Answer: O sits second to the right of Q.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix P (faces center) at position 1 (reference point)
- Q faces outward, sits third to the RIGHT of P:
P faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- O sits second to the LEFT of P (pos 1):
P faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
O faces same as Q → OUTWARD
- N faces center, sits immediately to the RIGHT of O (pos 7):
O faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- R immediately to the RIGHT of P(pos 1, center→CW): pos 2
- M opposite P(pos 1): pos 5
- S not adjacent to Q(pos 4): adj = pos 3 & 5
→ S at pos 8, T at pos 3

Final Arrangement (clockwise):
pos1:P(ctr) | pos2:R(out) | pos3:T(ctr) | pos4:Q(out) | pos5:M(out) | pos6:N(ctr) | pos7:O(out) | pos8:S(ctr)

Find second to the right of N (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = S

Verification:
✓ Q(outward) 3 left of P(center): 3 ACW from pos1 = pos4
✓ O 2nd left of P, same direction as Q (outward)
✓ N(center) immediately right of O(outward, right=ACW)
✓ R immediately right (CW) of P
✓ M opposite P
✓ S not adjacent to Q

Answer: S sits second to the right of N.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix S (faces center) at position 1 (reference point)
- R faces outward, sits third to the RIGHT of S:
S faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- Q sits second to the LEFT of S (pos 1):
S faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
Q faces same as R → OUTWARD
- M faces center, sits immediately to the RIGHT of Q (pos 7):
Q faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- O immediately to the RIGHT of S(pos 1, center→CW): pos 2
- T opposite S(pos 1): pos 5
- P not adjacent to R(pos 4): adj = pos 3 & 5
→ P at pos 8, N at pos 3

Final Arrangement (clockwise):
pos1:S(ctr) | pos2:O(out) | pos3:N(ctr) | pos4:R(out) | pos5:T(out) | pos6:M(ctr) | pos7:Q(out) | pos8:P(ctr)

Find second to the right of M (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = P

Verification:
✓ R(outward) 3 left of S(center): 3 ACW from pos1 = pos4
✓ Q 2nd left of S, same direction as R (outward)
✓ M(center) immediately right of Q(outward, right=ACW)
✓ O immediately right (CW) of S
✓ T opposite S
✓ P not adjacent to R

Answer: P sits second to the right of M.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix R (faces center) at position 1 (reference point)
- P faces outward, sits third to the RIGHT of R:
R faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- O sits second to the LEFT of R (pos 1):
R faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
O faces same as P → OUTWARD
- Q faces center, sits immediately to the RIGHT of O (pos 7):
O faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- T immediately to the RIGHT of R(pos 1, center→CW): pos 2
- S opposite R(pos 1): pos 5
- N not adjacent to P(pos 4): adj = pos 3 & 5
→ N at pos 8, M at pos 3

Final Arrangement (clockwise):
pos1:R(ctr) | pos2:T(out) | pos3:M(ctr) | pos4:P(out) | pos5:S(out) | pos6:Q(ctr) | pos7:O(out) | pos8:N(ctr)

Find second to the right of Q (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = N

Verification:
✓ P(outward) 3 left of R(center): 3 ACW from pos1 = pos4
✓ O 2nd left of R, same direction as P (outward)
✓ Q(center) immediately right of O(outward, right=ACW)
✓ T immediately right (CW) of R
✓ S opposite R
✓ N not adjacent to P

Answer: N sits second to the right of Q.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix R (faces center) at position 1 (reference point)
- Q faces outward, sits third to the RIGHT of R:
R faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- M sits second to the LEFT of R (pos 1):
R faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
M faces same as Q → OUTWARD
- O faces center, sits immediately to the RIGHT of M (pos 7):
M faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- P immediately to the RIGHT of R(pos 1, center→CW): pos 2
- T opposite R(pos 1): pos 5
- S not adjacent to Q(pos 4): adj = pos 3 & 5
→ S at pos 8, N at pos 3

Final Arrangement (clockwise):
pos1:R(ctr) | pos2:P(out) | pos3:N(ctr) | pos4:Q(out) | pos5:T(out) | pos6:O(ctr) | pos7:M(out) | pos8:S(ctr)

Find second to the right of O (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = S

Verification:
✓ Q(outward) 3 left of R(center): 3 ACW from pos1 = pos4
✓ M 2nd left of R, same direction as Q (outward)
✓ O(center) immediately right of M(outward, right=ACW)
✓ P immediately right (CW) of R
✓ T opposite R
✓ S not adjacent to Q

Answer: S sits second to the right of O.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix N (faces center) at position 1 (reference point)
- M faces outward, sits third to the RIGHT of N:
N faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- Q sits second to the LEFT of N (pos 1):
N faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
Q faces same as M → OUTWARD
- O faces center, sits immediately to the RIGHT of Q (pos 7):
Q faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- S immediately to the RIGHT of N(pos 1, center→CW): pos 2
- P opposite N(pos 1): pos 5
- T not adjacent to M(pos 4): adj = pos 3 & 5
→ T at pos 8, R at pos 3

Final Arrangement (clockwise):
pos1:N(ctr) | pos2:S(out) | pos3:R(ctr) | pos4:M(out) | pos5:P(out) | pos6:O(ctr) | pos7:Q(out) | pos8:T(ctr)

Find second to the right of O (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = T

Verification:
✓ M(outward) 3 left of N(center): 3 ACW from pos1 = pos4
✓ Q 2nd left of N, same direction as M (outward)
✓ O(center) immediately right of Q(outward, right=ACW)
✓ S immediately right (CW) of N
✓ P opposite N
✓ T not adjacent to M

Answer: T sits second to the right of O.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix T (faces center) at position 1 (reference point)
- R faces outward, sits third to the RIGHT of T:
T faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- P sits second to the LEFT of T (pos 1):
T faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
P faces same as R → OUTWARD
- S faces center, sits immediately to the RIGHT of P (pos 7):
P faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- O immediately to the RIGHT of T(pos 1, center→CW): pos 2
- Q opposite T(pos 1): pos 5
- M not adjacent to R(pos 4): adj = pos 3 & 5
→ M at pos 8, N at pos 3

Final Arrangement (clockwise):
pos1:T(ctr) | pos2:O(out) | pos3:N(ctr) | pos4:R(out) | pos5:Q(out) | pos6:S(ctr) | pos7:P(out) | pos8:M(ctr)

Find second to the right of S (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = M

Verification:
✓ R(outward) 3 left of T(center): 3 ACW from pos1 = pos4
✓ P 2nd left of T, same direction as R (outward)
✓ S(center) immediately right of P(outward, right=ACW)
✓ O immediately right (CW) of T
✓ Q opposite T
✓ M not adjacent to R

Answer: M sits second to the right of S.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix T (faces center) at position 1 (reference point)
- R faces outward, sits third to the RIGHT of T:
T faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- Q sits second to the LEFT of T (pos 1):
T faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
Q faces same as R → OUTWARD
- N faces center, sits immediately to the RIGHT of Q (pos 7):
Q faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- O immediately to the RIGHT of T(pos 1, center→CW): pos 2
- P opposite T(pos 1): pos 5
- M not adjacent to R(pos 4): adj = pos 3 & 5
→ M at pos 8, S at pos 3

Final Arrangement (clockwise):
pos1:T(ctr) | pos2:O(out) | pos3:S(ctr) | pos4:R(out) | pos5:P(out) | pos6:N(ctr) | pos7:Q(out) | pos8:M(ctr)

Find second to the right of N (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = M

Verification:
✓ R(outward) 3 left of T(center): 3 ACW from pos1 = pos4
✓ Q 2nd left of T, same direction as R (outward)
✓ N(center) immediately right of Q(outward, right=ACW)
✓ O immediately right (CW) of T
✓ P opposite T
✓ M not adjacent to R

Answer: M sits second to the right of N.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix T (faces center) at position 1 (reference point)
- M faces outward, sits third to the RIGHT of T:
T faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- O sits second to the LEFT of T (pos 1):
T faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
O faces same as M → OUTWARD
- N faces center, sits immediately to the RIGHT of O (pos 7):
O faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- R immediately to the RIGHT of T(pos 1, center→CW): pos 2
- Q opposite T(pos 1): pos 5
- S not adjacent to M(pos 4): adj = pos 3 & 5
→ S at pos 8, P at pos 3

Final Arrangement (clockwise):
pos1:T(ctr) | pos2:R(out) | pos3:P(ctr) | pos4:M(out) | pos5:Q(out) | pos6:N(ctr) | pos7:O(out) | pos8:S(ctr)

Find second to the right of N (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = S

Verification:
✓ M(outward) 3 left of T(center): 3 ACW from pos1 = pos4
✓ O 2nd left of T, same direction as M (outward)
✓ N(center) immediately right of O(outward, right=ACW)
✓ R immediately right (CW) of T
✓ Q opposite T
✓ S not adjacent to M

Answer: S sits second to the right of N.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix T (faces center) at position 1 (reference point)
- N faces outward, sits third to the RIGHT of T:
T faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- R sits second to the LEFT of T (pos 1):
T faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
R faces same as N → OUTWARD
- M faces center, sits immediately to the RIGHT of R (pos 7):
R faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- S immediately to the RIGHT of T(pos 1, center→CW): pos 2
- O opposite T(pos 1): pos 5
- P not adjacent to N(pos 4): adj = pos 3 & 5
→ P at pos 8, Q at pos 3

Final Arrangement (clockwise):
pos1:T(ctr) | pos2:S(out) | pos3:Q(ctr) | pos4:N(out) | pos5:O(out) | pos6:M(ctr) | pos7:R(out) | pos8:P(ctr)

Find second to the right of M (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = P

Verification:
✓ N(outward) 3 left of T(center): 3 ACW from pos1 = pos4
✓ R 2nd left of T, same direction as N (outward)
✓ M(center) immediately right of R(outward, right=ACW)
✓ S immediately right (CW) of T
✓ O opposite T
✓ P not adjacent to N

Answer: P sits second to the right of M.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix O (faces center) at position 1 (reference point)
- S faces outward, sits third to the RIGHT of O:
O faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- T sits second to the LEFT of O (pos 1):
O faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
T faces same as S → OUTWARD
- R faces center, sits immediately to the RIGHT of T (pos 7):
T faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- N immediately to the RIGHT of O(pos 1, center→CW): pos 2
- P opposite O(pos 1): pos 5
- M not adjacent to S(pos 4): adj = pos 3 & 5
→ M at pos 8, Q at pos 3

Final Arrangement (clockwise):
pos1:O(ctr) | pos2:N(out) | pos3:Q(ctr) | pos4:S(out) | pos5:P(out) | pos6:R(ctr) | pos7:T(out) | pos8:M(ctr)

Find second to the right of R (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = M

Verification:
✓ S(outward) 3 left of O(center): 3 ACW from pos1 = pos4
✓ T 2nd left of O, same direction as S (outward)
✓ R(center) immediately right of T(outward, right=ACW)
✓ N immediately right (CW) of O
✓ P opposite O
✓ M not adjacent to S

Answer: M sits second to the right of R.

Solution Approach:

Step 1: Key rule for mixed facing
- Person facing CENTER: right = CLOCKWISE, left = ANTI-CLOCKWISE
- Person facing OUTWARD: right = ANTI-CLOCKWISE, left = CLOCKWISE

Step 2: Draw 8-seat circle (positions 1–8 clockwise)

Step 3: Start with definite information
- Fix Q (faces center) at position 1 (reference point)
- R faces outward, sits third to the RIGHT of Q:
Q faces center → right = clockwise
3 CW from pos 1 → pos 4
N = pos 4 ✓

Step 4: Apply relative positions
- T sits second to the LEFT of Q (pos 1):
Q faces center → left = anti-clockwise
2 anti-CW from pos 1 → pos 7
T faces same as R → OUTWARD
- M faces center, sits immediately to the RIGHT of T (pos 7):
T faces outward → right = anti-clockwise
1 anti-CW from pos 7 → pos 6

Step 5: Fill remaining persons
- N immediately to the RIGHT of Q(pos 1, center→CW): pos 2
- P opposite Q(pos 1): pos 5
- O not adjacent to R(pos 4): adj = pos 3 & 5
→ O at pos 8, S at pos 3

Final Arrangement (clockwise):
pos1:Q(ctr) | pos2:N(out) | pos3:S(ctr) | pos4:R(out) | pos5:P(out) | pos6:M(ctr) | pos7:T(out) | pos8:O(ctr)

Find second to the right of M (pos 6, center-facing → CW):
2 CW from pos 6: → pos 8 = O

Verification:
✓ R(outward) 3 left of Q(center): 3 ACW from pos1 = pos4
✓ T 2nd left of Q, same direction as R (outward)
✓ M(center) immediately right of T(outward, right=ACW)
✓ N immediately right (CW) of Q
✓ P opposite Q
✓ O not adjacent to R

Answer: O sits second to the right of M.