Direction Sense

At a glance 10 rules

1. 1Left and right turnsA right turn is 90° clockwise, a left turn 90° anticlockwise. Net turn = (rights − lefts) × 90°, so two rights, or two lefts, reverse your direction.
2. 2Turns in degreesTake clockwise as + and anticlockwise as −, add, and reduce by 360°. Each 45° is one step round N, NE, E, SE, S, SW, W, NW.
3. 3ShadowsThe sun rises in the east, so a morning shadow points west and an evening shadow points east. Turn the side the shadow falls on into the way the person faces.
4. 4Clock as a compassLying face up, a clock turns like a compass, N to E. At h:m the hour hand is $30h + 0.5m$ degrees past 12 and the minute hand $6m$; turn from the known hand by the gap.
5. 5Net displacementAdd the moves on each axis separately: x = east − west, y = north − south. The path in between does not matter, only these two totals.
6. 6Distance and directionFor net moves x and y, distance is $\sqrt{x^2 + y^2}$ (know 3-4-5, 5-12-13, 8-15-17). Direction from the signs: east and north is NE; one zero total is straight N, E, S or W.
7. 7Start from the end'Where is the start from the end?' is the opposite direction: N and S swap, E and W, NE and SW, SE and NW. The distance stays the same.
8. 8Diagonal movesSplit a diagonal into its two parts: $d\sqrt{2}$ km north-east is d km east plus d km north. SE, SW and NW split the same way.
9. 9Two peopleFix both end points from the same origin, then subtract: the gap on each axis gives the distance and the direction between them. A shared first leg cancels.
10. 10Coded directionsWrite each code as an arrow ('P ★ Q': P is 8 km north of Q, read from P). Fix one letter at the origin and place every other letter from it, one code at a time.