Reasoning · Lesson 4

Directions & Ranking

Where will you end up after three turns? How many children stand in the line? Learn to draw every direction puzzle and count every row without a single slip.

~45 min read8 quick checksTest: 20 questions
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1The compass: 8 directions

There are four main (cardinal) directions: North, East, South, West. Halfway between them are four in-between (intercardinal) directions: North-East (NE), South-East (SE), South-West (SW), North-West (NW).

NNEESESSWWNW45° betweenneighbours
The purple arrow shows the clockwise direction. On maps and in puzzles, North is up, East is right, South is down and West is left. Going clockwise from North: N, NE, E, SE, S, SW, W, NW.
Remember the clockwise order N → E → S → W: “Naughty Elephants Spray Water”. And for left and right on a map, read West-to-East like a word: W E spells “we” — West on the left, East on the right.

2Turning left and right

A right turn is a quarter turn clockwise (90°). A left turn is a quarter turn anticlockwise (90°). An about turn is 180° — you face the opposite way.

Facing NorthR → EastL → WestFacing EastR → SouthL → NorthFacing SouthR → WestL → EastFacing WestR → NorthL → SouthMap rule: North is always up, East is always right
Your right and left depend on which way you are facing. When you face South, your right hand points West and your left hand points East.
FacingTurn right →Turn left →About turn →
NorthEastWestSouth
EastSouthNorthWest
SouthWestEastNorth
WestNorthSouthEast
⚠️ Olympiad trap: facing South

Most mistakes happen when someone faces South or West. Don't use the paper's left and right! Put your finger on the direction you face and turn the paper (or your body) so that direction points away from you. Facing South, a right turn goes West, a left turn goes East.

Turning by degrees

✏️ Worked example

Arun is facing East. He turns 45° anticlockwise, then makes an about turn. Which way is he facing now?

  1. 45° anticlockwise from East is one step back towards North: North-East.
  2. An about turn (180°) points to the opposite direction of NE: South-West.
✏️ Worked example

Neha faces West. She turns left, then left again, then right. Which way does she face?

  1. Facing West, a left turn → South.
  2. Facing South, a left turn → East.
  3. Facing East, a right turn → South. She faces South.
💡 Shortcut

Count turns: a left and a right cancel out. Two lefts (or two rights) = an about turn. In Neha's example: left + left + right = one left in total. West turned left once = South. ✔

Tanvi is facing West. She turns to her right. Which way is she facing now?

  1. South
  2. North
  3. East
  4. West
A right turn is a quarter turn clockwise. Clockwise from West comes North (W → NW → N).

Kunal faces North and turns 135° clockwise. Which way does he face now?

  1. South-East
  2. North-East
  3. South-West
  4. East
135° = 90° + 45°. From North, 90° clockwise is East; 45° more is South-East.

3Sunrise, sunset and shadows

The Sun rises in the East and sets in the West (roughly — it shifts a little with the seasons, but puzzles use exact East and West). A shadow always falls on the side opposite the Sun.

MorningWestEastshadow → WestEveningWestEastshadow → East
Morning: Sun in the East → shadow points West. Evening: Sun in the West → shadow points East. Around noon the Sun is high and shadows are shortest.
📌 Remember

Morning shadow → West. Evening shadow → East. Then use the turning table: which side of the person is West (or East)?

✏️ Worked example

In the morning, Riya stands facing North. On which side of her does her shadow fall?

  1. Morning → the Sun is in the East → the shadow falls towards the West.
  2. Facing North, West is on her left.
  3. Her shadow falls to her left.
✏️ Worked example

One evening, Aman's shadow falls exactly to his right. Which way is he facing?

  1. Evening → the Sun is in the West → the shadow points East.
  2. So East must be on Aman's right. Whose right is East? Someone facing North.
  3. Aman is facing North.

In the evening, Riya's shadow falls exactly behind her. Which direction is she facing?

  1. North
  2. East
  3. West
  4. South
Evening shadows point East. If East is behind her, she is facing West — looking towards the setting Sun.

4Walks: distance and final direction

For every walking puzzle, draw the path. Start with a dot, draw North up, and turn at each step using the direction you are facing.

  1. Mark the start. Draw a tiny “N ↑” in the corner.
  2. Draw each walk as an arrow with its length. Before each turn, ask “Which way am I facing now?”
  3. To find the final position, add up North–South and East–West separately. Opposite moves cancel.
  4. Answer the question asked: distance from start, direction from start, or direction facing.
✏️ Worked example

Tara walks 7 m North, turns right and walks 4 m, then turns right again and walks 7 m. How far is she from the start, and in which direction?

  1. Facing North, walk 7 m. Turn right → now facing East; walk 4 m.
  2. Facing East, turn right → now facing South; walk 7 m.
  3. North–South: 7 up, 7 down → cancels to 0. East–West: 4 East.
  4. She is 4 m East of the start (and she is facing South).
9 N7 E9 S3 WStartEndN
A bird flies 9 km North, 7 km East, 9 km South and 3 km West. North and South cancel; East − West = 7 − 3 = 4. It ends 4 km East of the start.
✏️ Worked example (final direction)

Dev walks 6 m North, turns right and walks 8 m, turns right and walks 3 m, then turns left and walks 4 m. In which direction is he from the start?

  1. 6 m North. Right turn → facing East, 8 m.
  2. Right turn → facing South, 3 m. Left turn (from South) → facing East, 4 m.
  3. North–South: 6 North − 3 South = 3 North. East–West: 8 + 4 = 12 East.
  4. He is North and East of the start → North-East.
6 N8 E3 S4 EStartEndN
Dev's walk. The dashed line joins start to end: it points up and to the right, which is North-East.
✏️ Worked example

Sam walks 6 km South, then 8 km West. In which direction is he from his starting point?

  1. He is 6 km South and 8 km West of the start.
  2. South + West → South-West.
6 S8 WStartEndN
6 km South, then 8 km West: the end point is South-West of the start. (Fun fact: the straight dashed line is exactly 10 km long.)
⚠️ Olympiad trap: which question is asked?

“In which direction is he facing?” and “In which direction is he from the start?” have different answers! Tara (above) is facing South but is East of the start. Also, the distance from the start is not the total distance walked (Tara walked 18 m but is only 4 m away).

Ravi walks 10 m East, turns left and walks 6 m, then turns left again and walks 10 m. Where is he now from his starting point?

  1. 6 m South
  2. 6 m North
  3. 10 m West
  4. 16 m North
Facing East, a left turn faces North (6 m). Facing North, a left turn faces West (10 m). East 10 and West 10 cancel, leaving 6 m North.

5Ranking in a row, queue or class

Position can be counted from either end: left or right in a row, front or back in a queue, top or bottom in a class. One person has two positions — one from each end.

111210394857667584931021114th from left8th from rightTotal = 4 + 8 − 1 = 11 (she is counted twice)
Count from the left and she is 4th; count from the right and she is 8th. She is counted in both counts, so subtract 1 once.
To find…UseExample
Total peopleLeft + Right − 17th from left, 12th from right → 7 + 12 − 1 = 18
Position from the other endTotal − position + 130 in a queue, 10th from front → 30 − 10 + 1 = 21st from back
People ahead / abovePosition − 114th from top → 13 above
People behind / belowTotal − position35 students, 9th from top → 35 − 9 = 26 below
People between two (same end)Bigger − smaller − 15th and 15th from left → 15 − 5 − 1 = 9
Remember “minus one, plus one”: joining two counts into a total → − 1 (you counted the person twice). Turning a total back into a position from the other end → + 1 (you must count the person too).
⚠️ Olympiad trap

“9th from the left and 8th from the right” — the quick answer 9 + 8 = 17 is wrong. The person is inside both counts, so the total is 9 + 8 − 1 = 16. And “12th from the top in a class of 40” is 29th from the bottom (40 − 12 + 1), not 28th.

✏️ Worked example (between two people)

In a row of 20 children, Asha is 5th from the left and Bala is 6th from the right. How many children are between them?

  1. Change Bala to “from the left”: 20 − 6 + 1 = 15th from the left.
  2. Asha is 5th, Bala is 15th (both from the left).
  3. Between them: 15 − 5 − 1 = 9 children.
✏️ Worked example (olympiad level: crossing over)

In a row of 18, Anil is 12th from the left and Bina is 10th from the right. How many children are between them?

  1. Bina from the left: 18 − 10 + 1 = 9th. So Bina is to the left of Anil!
  2. Positions 9 (Bina) and 12 (Anil): between = 12 − 9 − 1 = 2 (positions 10 and 11).
✏️ Worked example (moving along the row)

In a row of 20, Karan is 6th from the left. Leela is 4th to the right of Karan. What is Leela's position from the right end?

  1. Leela from the left: 6 + 4 = 10th.
  2. From the right: 20 − 10 + 1 = 11th.
✏️ Worked example (swapping places)

In a row, Anu is 5th from the left and Binu is 8th from the right. They swap places, and now Anu is 12th from the left. How many are in the row?

  1. After the swap, Anu stands exactly where Binu stood. So Binu's old place was 12th from the left.
  2. That same place is 8th from the right (Binu's old right position).
  3. Total = 12 + 8 − 1 = 19.

Meera is 11th from the left and 9th from the right in a row. How many children are in the row?

  1. 20
  2. 18
  3. 19
  4. 21
Total = 11 + 9 − 1 = 19. Meera is counted in both 11 and 9, so take away 1.

In a class of 45, Sonu is 17th from the top. What is his rank from the bottom?

  1. 28th
  2. 29th
  3. 30th
  4. 27th
From the bottom = 45 − 17 + 1 = 29th. (28 is the number of students below him.)

In a row of 30, Asha is 8th from the left and Bina is 10th from the right. How many children are between them?

  1. 12
  2. 13
  3. 11
  4. 14
Bina from the left = 30 − 10 + 1 = 21st. Between 8th and 21st: 21 − 8 − 1 = 12.

6Taller, heavier, older: ordering puzzles

For “A is taller than B…” puzzles, draw a ladder: the biggest at the top, the smallest at the bottom. Place each clue one at a time.

✏️ Worked example

A is taller than B. C is shorter than B. D is taller than A. Who is the shortest?

  1. “A is taller than B” → A above B.
  2. “C is shorter than B” → C below B: A, B, C.
  3. “D is taller than A” → D on top: D, A, B, C.
  4. Shortest: C.
DABCtallestshortestD > A > B > C
The finished ladder: D is the tallest and C the shortest.
✏️ Worked example (five people)

Vani is shorter than Ushma but taller than Wasim. Xena is taller than Ushma. Yash is the shortest. Who is in the middle?

  1. Ushma > Vani > Wasim.
  2. Xena > Ushma → Xena, Ushma, Vani, Wasim.
  3. Yash is the shortest → Xena, Ushma, Vani, Wasim, Yash.
  4. The middle (3rd) is Vani.
⚠️ Olympiad trap: “cannot be determined”

“A is taller than B. A is taller than C. Who is the shortest?” We know A is the tallest, but we are never told how B and C compare. The answer is “cannot be determined”. Only choose this option when a clue is truly missing.

💡 Tip

Words to watch: heavier/lighter, older/younger, more/fewer marks. “Lighter than” puts someone below on the weight ladder. Rewrite every clue in the same direction (“taller than”) before drawing.

Anil is older than Bala. Chetan is older than Anil. Deepa is younger than Bala. Who is the second youngest?

  1. Anil
  2. Deepa
  3. Chetan
  4. Bala
Oldest to youngest: Chetan, Anil, Bala, Deepa. The youngest is Deepa, so the second youngest is Bala.

7Sitting in a row

Draw the seats as boxes. Fill the sure clues first (“at the left end”, “in the middle”), then the clues that link two people.

✏️ Worked example

Five children sit in a row facing North. Maya sits at the right end. Kabir is 2nd from the left. Leela sits between Kabir and Nina. Om sits at the left end. Who sits in the middle?

  1. Sure clues: Om at seat 1 (left end), Kabir at seat 2, Maya at seat 5 (right end).
  2. Seats 3 and 4 are left for Leela and Nina. Leela is between Kabir and Nina, so Leela = seat 3, Nina = seat 4.
  3. Row: Om, Kabir, Leela, Nina, Maya. Middle: Leela.
Om1Kabir2Leela3Nina4Maya5all face North← left endright end →
Facing North, the children's left and right are the same as yours on the page. Nina is to Leela's immediate right.
⚠️ Olympiad trap: facing you

If people sit facing South (towards you), their right hand is on your left. Imagine sitting in their seat, facing their way, before you decide who is on whose right.

8Watch and explore

9Quick recap

Flip cards

QuestionOpposite of North-West?
AnswerSouth-East
QuestionFacing East, turn left twice. Now facing?
AnswerWest (two lefts = about turn)
QuestionMorning, facing South. Shadow on which side?
AnswerRight side (shadow points West)
Question10th from front, 6th from back. Total?
Answer15 (10 + 6 − 1)
QuestionClass of 50, 20th from top. From bottom?
Answer31st (50 − 20 + 1)
Question5 km N, 5 km E, 5 km S. Where from start?
Answer5 km East
QuestionFacing North, turn 270° clockwise. Now facing?
AnswerWest (same as one left turn)
Question7th and 18th from the left. How many between?
Answer10 (18 − 7 − 1)