If South-east is called East, North-west is called West, South-west is called South and so-on, what will North be called?

Correct — C, North-west. Put the eight compass points on a dial, measuring clockwise from north: north 0, north-east 45, east 90, south-east 135, south 180, south-west 225, west 270, north-west 315. Now read the three examples the stem gives. South-east, at 135, is called east, which sits at 90. North-west, at 315, is called west, at 270. South-west, at 225, is called south, at 180. Every one of them drops by exactly 45 degrees, so the rule is that each direction takes the name of the point 45 degrees anticlockwise of itself. Apply it to north, at 0 or equivalently 360: 360 minus 45 is 315, which is north-west. So under this scheme north is called north-west.

• (a)East — East is already the name given to south-east, as the stem itself states. A single name cannot belong to two directions in a one-to-one relabelling.
• (b)North-east — This is the answer for a rule that runs the other way, 45 degrees clockwise. Under the rule the stem actually gives, north-east is the direction that is called north.
• (d)South — South is the name already assigned to south-west. It also sits 180 degrees from north, which no 45-degree shift can reach.

A direction-renaming puzzle is a rotation of the naming scheme, and every such rotation is a fixed number of 45-degree steps around the eight-point compass. The work is to read one or two of the given examples, measure the step, and confirm it against the remaining examples before applying it. Confirming against a second example is what protects against reading the rotation in the wrong sense.

The direction of the shift is the whole item, and the option list is built so that both senses of rotation appear. Writing the eight points in a ring and moving one step round is more reliable under time pressure than reasoning in degrees. Note also the consistency check the stem hands you free of charge: since east, west and south have already been used as names, none of them can be the name of north, which removes two options before any rotation is worked out.

• The eight compass points sit at 45-degree intervals: N 0, NE 45, E 90, SE 135, S 180, SW 225, W 270, NW 315.
• Each of the three given examples shifts by exactly 45 degrees anticlockwise: SE to E, NW to W, SW to S.
• Applying the same shift to north at 360 degrees gives 315 degrees, which is north-west.
• The full relabelling runs N to NW, NE to N, E to NE, SE to E, S to SE, SW to S, W to SW, NW to W.
• In a one-to-one renaming, a name already used for one direction cannot be reused for another.

• Rotating clockwise instead of anticlockwise and answering north-east.
• Assigning a name that the stem has already used for a different direction.
• Working from a single example without checking the rule against the other two.

Asked as a rotation puzzle with three worked examples supplied, so the only error available is reading the rotation the wrong way round.

• practice — not a real PYQ

  In the same scheme, where south-east is called east and south-west is called south, what will east be called?

  • (a)North
  • (b)North-east
  • (c)South-east
  • (d)West

  Answer(b) North-east — east at 90 degrees takes the name of the point 45 degrees anticlockwise, which is north-east at 45.

• practice — not a real PYQ

  If north is called south, south is called east and east is called west, in which direction does the sun rise under this scheme?

  • (a)North
  • (b)South
  • (c)East
  • (d)West

  Answer(d) West — the sun rises in the physical east, and east is called west in this scheme.