Circular Facing Outward - Expert Level: conceptual clarity Circular Facing Outward EXPERT

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix L at position 1.
- N sits second to the LEFT of L: left(outward)=CW, so N is 2 CW from L.
pos[N] = 3
- M sits opposite N (pos 3): pos 6
- K sits immediately to the RIGHT of M (pos 6):
right(outward)=anti-CW → pos 5
- P sits opposite L (pos 1): pos 4
- Remaining O fills pos 2.

Final Arrangement (clockwise):
pos1:L → pos2:O → pos3:N → pos4:P → pos5:K → pos6:M
(All facing outward ↗)

Find immediate left of N (pos 3):
Left (outward) = clockwise → pos 4 = P

Verification:
✓ N second to left of L (CW direction)
✓ M opposite N
✓ K immediately right (anti-CW) of M
✓ P opposite L

Answer: P sits immediately to the left of N.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix M at position 1.
- L sits second to the LEFT of M: left(outward)=CW, so L is 2 CW from M.
pos[L] = 3
- O sits opposite L (pos 3): pos 6
- P sits immediately to the RIGHT of O (pos 6):
right(outward)=anti-CW → pos 5
- N sits opposite M (pos 1): pos 4
- Remaining K fills pos 2.

Final Arrangement (clockwise):
pos1:M → pos2:K → pos3:L → pos4:N → pos5:P → pos6:O
(All facing outward ↗)

Find immediate left of L (pos 3):
Left (outward) = clockwise → pos 4 = N

Verification:
✓ L second to left of M (CW direction)
✓ O opposite L
✓ P immediately right (anti-CW) of O
✓ N opposite M

Answer: N sits immediately to the left of L.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix M at position 1.
- O sits second to the LEFT of M: left(outward)=CW, so O is 2 CW from M.
pos[O] = 3
- L sits opposite O (pos 3): pos 6
- K sits immediately to the RIGHT of L (pos 6):
right(outward)=anti-CW → pos 5
- N sits opposite M (pos 1): pos 4
- Remaining P fills pos 2.

Final Arrangement (clockwise):
pos1:M → pos2:P → pos3:O → pos4:N → pos5:K → pos6:L
(All facing outward ↗)

Find immediate left of O (pos 3):
Left (outward) = clockwise → pos 4 = N

Verification:
✓ O second to left of M (CW direction)
✓ L opposite O
✓ K immediately right (anti-CW) of L
✓ N opposite M

Answer: N sits immediately to the left of O.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix K at position 1.
- N sits second to the LEFT of K: left(outward)=CW, so N is 2 CW from K.
pos[N] = 3
- O sits opposite N (pos 3): pos 6
- P sits immediately to the RIGHT of O (pos 6):
right(outward)=anti-CW → pos 5
- M sits opposite K (pos 1): pos 4
- Remaining L fills pos 2.

Final Arrangement (clockwise):
pos1:K → pos2:L → pos3:N → pos4:M → pos5:P → pos6:O
(All facing outward ↗)

Find immediate left of N (pos 3):
Left (outward) = clockwise → pos 4 = M

Verification:
✓ N second to left of K (CW direction)
✓ O opposite N
✓ P immediately right (anti-CW) of O
✓ M opposite K

Answer: M sits immediately to the left of N.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix K at position 1.
- O sits second to the LEFT of K: left(outward)=CW, so O is 2 CW from K.
pos[O] = 3
- L sits opposite O (pos 3): pos 6
- N sits immediately to the RIGHT of L (pos 6):
right(outward)=anti-CW → pos 5
- P sits opposite K (pos 1): pos 4
- Remaining M fills pos 2.

Final Arrangement (clockwise):
pos1:K → pos2:M → pos3:O → pos4:P → pos5:N → pos6:L
(All facing outward ↗)

Find immediate left of O (pos 3):
Left (outward) = clockwise → pos 4 = P

Verification:
✓ O second to left of K (CW direction)
✓ L opposite O
✓ N immediately right (anti-CW) of L
✓ P opposite K

Answer: P sits immediately to the left of O.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix K at position 1.
- M sits second to the LEFT of K: left(outward)=CW, so M is 2 CW from K.
pos[M] = 3
- O sits opposite M (pos 3): pos 6
- N sits immediately to the RIGHT of O (pos 6):
right(outward)=anti-CW → pos 5
- P sits opposite K (pos 1): pos 4
- Remaining L fills pos 2.

Final Arrangement (clockwise):
pos1:K → pos2:L → pos3:M → pos4:P → pos5:N → pos6:O
(All facing outward ↗)

Find immediate left of M (pos 3):
Left (outward) = clockwise → pos 4 = P

Verification:
✓ M second to left of K (CW direction)
✓ O opposite M
✓ N immediately right (anti-CW) of O
✓ P opposite K

Answer: P sits immediately to the left of M.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix L at position 1.
- P sits second to the LEFT of L: left(outward)=CW, so P is 2 CW from L.
pos[P] = 3
- O sits opposite P (pos 3): pos 6
- N sits immediately to the RIGHT of O (pos 6):
right(outward)=anti-CW → pos 5
- K sits opposite L (pos 1): pos 4
- Remaining M fills pos 2.

Final Arrangement (clockwise):
pos1:L → pos2:M → pos3:P → pos4:K → pos5:N → pos6:O
(All facing outward ↗)

Find immediate left of P (pos 3):
Left (outward) = clockwise → pos 4 = K

Verification:
✓ P second to left of L (CW direction)
✓ O opposite P
✓ N immediately right (anti-CW) of O
✓ K opposite L

Answer: K sits immediately to the left of P.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix M at position 1.
- K sits second to the LEFT of M: left(outward)=CW, so K is 2 CW from M.
pos[K] = 3
- N sits opposite K (pos 3): pos 6
- L sits immediately to the RIGHT of N (pos 6):
right(outward)=anti-CW → pos 5
- O sits opposite M (pos 1): pos 4
- Remaining P fills pos 2.

Final Arrangement (clockwise):
pos1:M → pos2:P → pos3:K → pos4:O → pos5:L → pos6:N
(All facing outward ↗)

Find immediate left of K (pos 3):
Left (outward) = clockwise → pos 4 = O

Verification:
✓ K second to left of M (CW direction)
✓ N opposite K
✓ L immediately right (anti-CW) of N
✓ O opposite M

Answer: O sits immediately to the left of K.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix O at position 1.
- P sits second to the LEFT of O: left(outward)=CW, so P is 2 CW from O.
pos[P] = 3
- K sits opposite P (pos 3): pos 6
- M sits immediately to the RIGHT of K (pos 6):
right(outward)=anti-CW → pos 5
- L sits opposite O (pos 1): pos 4
- Remaining N fills pos 2.

Final Arrangement (clockwise):
pos1:O → pos2:N → pos3:P → pos4:L → pos5:M → pos6:K
(All facing outward ↗)

Find immediate left of P (pos 3):
Left (outward) = clockwise → pos 4 = L

Verification:
✓ P second to left of O (CW direction)
✓ K opposite P
✓ M immediately right (anti-CW) of K
✓ L opposite O

Answer: L sits immediately to the left of P.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix O at position 1.
- L sits second to the LEFT of O: left(outward)=CW, so L is 2 CW from O.
pos[L] = 3
- N sits opposite L (pos 3): pos 6
- K sits immediately to the RIGHT of N (pos 6):
right(outward)=anti-CW → pos 5
- P sits opposite O (pos 1): pos 4
- Remaining M fills pos 2.

Final Arrangement (clockwise):
pos1:O → pos2:M → pos3:L → pos4:P → pos5:K → pos6:N
(All facing outward ↗)

Find immediate left of L (pos 3):
Left (outward) = clockwise → pos 4 = P

Verification:
✓ L second to left of O (CW direction)
✓ N opposite L
✓ K immediately right (anti-CW) of N
✓ P opposite O

Answer: P sits immediately to the left of L.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix O at position 1.
- M sits second to the LEFT of O: left(outward)=CW, so M is 2 CW from O.
pos[M] = 3
- N sits opposite M (pos 3): pos 6
- K sits immediately to the RIGHT of N (pos 6):
right(outward)=anti-CW → pos 5
- L sits opposite O (pos 1): pos 4
- Remaining P fills pos 2.

Final Arrangement (clockwise):
pos1:O → pos2:P → pos3:M → pos4:L → pos5:K → pos6:N
(All facing outward ↗)

Find immediate left of M (pos 3):
Left (outward) = clockwise → pos 4 = L

Verification:
✓ M second to left of O (CW direction)
✓ N opposite M
✓ K immediately right (anti-CW) of N
✓ L opposite O

Answer: L sits immediately to the left of M.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix O at position 1.
- K sits second to the LEFT of O: left(outward)=CW, so K is 2 CW from O.
pos[K] = 3
- N sits opposite K (pos 3): pos 6
- P sits immediately to the RIGHT of N (pos 6):
right(outward)=anti-CW → pos 5
- L sits opposite O (pos 1): pos 4
- Remaining M fills pos 2.

Final Arrangement (clockwise):
pos1:O → pos2:M → pos3:K → pos4:L → pos5:P → pos6:N
(All facing outward ↗)

Find immediate left of K (pos 3):
Left (outward) = clockwise → pos 4 = L

Verification:
✓ K second to left of O (CW direction)
✓ N opposite K
✓ P immediately right (anti-CW) of N
✓ L opposite O

Answer: L sits immediately to the left of K.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix L at position 1.
- K sits second to the LEFT of L: left(outward)=CW, so K is 2 CW from L.
pos[K] = 3
- O sits opposite K (pos 3): pos 6
- P sits immediately to the RIGHT of O (pos 6):
right(outward)=anti-CW → pos 5
- N sits opposite L (pos 1): pos 4
- Remaining M fills pos 2.

Final Arrangement (clockwise):
pos1:L → pos2:M → pos3:K → pos4:N → pos5:P → pos6:O
(All facing outward ↗)

Find immediate left of K (pos 3):
Left (outward) = clockwise → pos 4 = N

Verification:
✓ K second to left of L (CW direction)
✓ O opposite K
✓ P immediately right (anti-CW) of O
✓ N opposite L

Answer: N sits immediately to the left of K.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix L at position 1.
- P sits second to the LEFT of L: left(outward)=CW, so P is 2 CW from L.
pos[P] = 3
- N sits opposite P (pos 3): pos 6
- O sits immediately to the RIGHT of N (pos 6):
right(outward)=anti-CW → pos 5
- M sits opposite L (pos 1): pos 4
- Remaining K fills pos 2.

Final Arrangement (clockwise):
pos1:L → pos2:K → pos3:P → pos4:M → pos5:O → pos6:N
(All facing outward ↗)

Find immediate left of P (pos 3):
Left (outward) = clockwise → pos 4 = M

Verification:
✓ P second to left of L (CW direction)
✓ N opposite P
✓ O immediately right (anti-CW) of N
✓ M opposite L

Answer: M sits immediately to the left of P.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix P at position 1.
- O sits second to the LEFT of P: left(outward)=CW, so O is 2 CW from P.
pos[O] = 3
- M sits opposite O (pos 3): pos 6
- L sits immediately to the RIGHT of M (pos 6):
right(outward)=anti-CW → pos 5
- N sits opposite P (pos 1): pos 4
- Remaining K fills pos 2.

Final Arrangement (clockwise):
pos1:P → pos2:K → pos3:O → pos4:N → pos5:L → pos6:M
(All facing outward ↗)

Find immediate left of O (pos 3):
Left (outward) = clockwise → pos 4 = N

Verification:
✓ O second to left of P (CW direction)
✓ M opposite O
✓ L immediately right (anti-CW) of M
✓ N opposite P

Answer: N sits immediately to the left of O.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix P at position 1.
- M sits second to the LEFT of P: left(outward)=CW, so M is 2 CW from P.
pos[M] = 3
- O sits opposite M (pos 3): pos 6
- N sits immediately to the RIGHT of O (pos 6):
right(outward)=anti-CW → pos 5
- K sits opposite P (pos 1): pos 4
- Remaining L fills pos 2.

Final Arrangement (clockwise):
pos1:P → pos2:L → pos3:M → pos4:K → pos5:N → pos6:O
(All facing outward ↗)

Find immediate left of M (pos 3):
Left (outward) = clockwise → pos 4 = K

Verification:
✓ M second to left of P (CW direction)
✓ O opposite M
✓ N immediately right (anti-CW) of O
✓ K opposite P

Answer: K sits immediately to the left of M.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix M at position 1.
- L sits second to the LEFT of M: left(outward)=CW, so L is 2 CW from M.
pos[L] = 3
- P sits opposite L (pos 3): pos 6
- K sits immediately to the RIGHT of P (pos 6):
right(outward)=anti-CW → pos 5
- N sits opposite M (pos 1): pos 4
- Remaining O fills pos 2.

Final Arrangement (clockwise):
pos1:M → pos2:O → pos3:L → pos4:N → pos5:K → pos6:P
(All facing outward ↗)

Find immediate left of L (pos 3):
Left (outward) = clockwise → pos 4 = N

Verification:
✓ L second to left of M (CW direction)
✓ P opposite L
✓ K immediately right (anti-CW) of P
✓ N opposite M

Answer: N sits immediately to the left of L.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix L at position 1.
- K sits second to the LEFT of L: left(outward)=CW, so K is 2 CW from L.
pos[K] = 3
- O sits opposite K (pos 3): pos 6
- M sits immediately to the RIGHT of O (pos 6):
right(outward)=anti-CW → pos 5
- P sits opposite L (pos 1): pos 4
- Remaining N fills pos 2.

Final Arrangement (clockwise):
pos1:L → pos2:N → pos3:K → pos4:P → pos5:M → pos6:O
(All facing outward ↗)

Find immediate left of K (pos 3):
Left (outward) = clockwise → pos 4 = P

Verification:
✓ K second to left of L (CW direction)
✓ O opposite K
✓ M immediately right (anti-CW) of O
✓ P opposite L

Answer: P sits immediately to the left of K.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix L at position 1.
- M sits second to the LEFT of L: left(outward)=CW, so M is 2 CW from L.
pos[M] = 3
- P sits opposite M (pos 3): pos 6
- N sits immediately to the RIGHT of P (pos 6):
right(outward)=anti-CW → pos 5
- O sits opposite L (pos 1): pos 4
- Remaining K fills pos 2.

Final Arrangement (clockwise):
pos1:L → pos2:K → pos3:M → pos4:O → pos5:N → pos6:P
(All facing outward ↗)

Find immediate left of M (pos 3):
Left (outward) = clockwise → pos 4 = O

Verification:
✓ M second to left of L (CW direction)
✓ P opposite M
✓ N immediately right (anti-CW) of P
✓ O opposite L

Answer: O sits immediately to the left of M.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix O at position 1.
- N sits second to the LEFT of O: left(outward)=CW, so N is 2 CW from O.
pos[N] = 3
- L sits opposite N (pos 3): pos 6
- K sits immediately to the RIGHT of L (pos 6):
right(outward)=anti-CW → pos 5
- P sits opposite O (pos 1): pos 4
- Remaining M fills pos 2.

Final Arrangement (clockwise):
pos1:O → pos2:M → pos3:N → pos4:P → pos5:K → pos6:L
(All facing outward ↗)

Find immediate left of N (pos 3):
Left (outward) = clockwise → pos 4 = P

Verification:
✓ N second to left of O (CW direction)
✓ L opposite N
✓ K immediately right (anti-CW) of L
✓ P opposite O

Answer: P sits immediately to the left of N.