Direction questions ask which way you end up facing, and how far you really are from where you started. Ranking questions ask where a person stands in a line. Both topics have one clean formula each — once you know it, you never have to guess.
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Going clockwise, the order is always North → East → South → West and back to North.
A right turn (90°) moves you one step clockwise: North → East → South → West → North.
A left turn (90°) moves you one step the other way.
A full U-turn is two right turns (180°). North becomes South, East becomes West — always the exact opposite direction.
Walking the same direction twice? Add the distances. Walking opposite directions? Subtract them.
The shortest-distance trap: if you walk in two directions that are exactly perpendicular (like East then North), the straight-line distance back to the start is NOT the sum — you need the two legs to form a 3-4-5 (or 6-8-10, or 9-12-15) triangle to get a whole-number answer.
In a line of people, "from the left" and "from the right" are two different ways of counting the same line.
The two ranking formulas
Position from the other end = Total people − Position you know + 1
Total people (when you know a position from both ends) = Position from left + Position from right − 1
People standing between two people (counted from the same end) = the difference between their positions, minus 1
12 IMO-style questions. Draw the path or the line on rough paper before you answer! 🍀
