39Directions: Read the information and answer the given questions. A * B (18m)…

In a coded direction-and-distance puzzle, every statement of the form 'A [symbol] B (n m)' encodes two things at once: a compass direction, and a fixed rule that converts the printed bracket figure into the real straight-line displacement between A and B. Once the direction each symbol stands for, and the size of the conversion offset, are read off the defining examples, every point named in the passage can be plotted on a standard grid (north = up, east = right), and the distance between any two points follows by adding displacement vectors along the chain of statements that connects them.

• 'A * B (18m) means A is 8m north of B' fixes '*' = north, with offset 18 - 8 = 10 m.

• 'A% B (24m) means A is 14m south of B' fixes '%' = south, with offset 24 - 14 = 10 m.

• 'A & B (28m) means A is 18m east of B' fixes '&' = east, with offset 28 - 18 = 10 m.

• 'A @ B (35m) means A is 25m west of B' fixes '@' = west, with offset 35 - 25 = 10 m.

So for every relation in the list, actual distance = printed figure - 10 m.

1. The two relations that connect U directly to X are 'R * U (22m)', which gives R is (22 - 10) = 12 m north of U, and 'X * R (30m)', which gives X is (30 - 10) = 20 m north of R.

2. Place U at the origin (0, 0). Since R is 12 m north of U, R is at (0, 12).

3. Since X is 20 m north of R, X is at (0, 12 + 20) = (0, 32).

4. U and X share the same horizontal coordinate (both lie at x = 0), so the straight-line distance between them is simply the difference of their vertical coordinates: 32 - 0 = 32 m.

Adding the two legs directly, without coordinates, confirms this: from U to R is 12 m north, and from R to X is a further 20 m north - both legs point the same way, so they add rather than cancel: 12 m + 20 m = 32 m, the same total.

The distance between U and X is 32 m.