Question

Directions for questions 49 to 52: There are exactly ten stores and no other buildings on a straight street in Bistupur Market. On the northern side of the street, from west to east, are stores 1, 3, 5, 7, and 9. On the southern side, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the northern side sit directly across the street from the stores on the southern side, facing each other in pairs: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10.

Each store is decorated with lights in exactly one colour: green, red, or yellow. The lighting follows these rules:
1. No store has the same light colour as a store next to it on the same side of the street.
2. No store has the same light colour as the store directly across the street from it.
3. Yellow lights decorate exactly one store on each side of the street.
4. Store 4 has red lights.
5. Store 5 has yellow lights.

Which one of the following statements MUST be true?

• A. Green lights decorate store 10
• B. Red lights decorate store 1
• C. Red lights decorate store 8
• D. Yellow lights decorate store 8

Hint:

Trace store 1's two constraints separately: what colour blocks it from being green, and what already uses up the one yellow slot on its side of the street.

Answer 1

The Correct Option is B

A "must be true" question is really asking: is there any valid way to colour the street where this statement fails? If yes, the statement is not forced. If every valid colouring agrees on it, the statement must be true. Let's build up the picture of the street store by store and then test each option against it.

1. Green lights decorate store 10: store 10 only has to avoid matching store 8 (its neighbour) and store 9 (the store it faces). Nothing pins it to green specifically. For example, if store 9 ends up red and store 8 ends up red, store 10 is free to be green or yellow; if store 8 ends up yellow, store 10 could be red or green. Since more than one colour works for store 10 across different valid completions of the puzzle, it is not forced to be green.
2. Red lights decorate store 1: store 1 sits next to store 3 on the same side, and store 3 is forced to green because it neighbours red store 4 and faces yellow store 5. So store 1 cannot be green (its neighbour store 3 already has that colour). Store 1 also cannot be yellow, because the only yellow slot allowed on the north side is already used by store 5. With green and yellow both closed off, red is the only colour left for store 1, and this reasoning uses nothing beyond the five original rules, so it holds no matter what happens elsewhere on the street.
3. Red lights decorate store 8: store 8 must differ from store 6 (green) and from store 7 (whatever store 7 turns out to be, green or red). If store 7 is red, store 8 is free to be green or yellow, not red. So store 8 is not always red.
4. Yellow lights decorate store 8: similarly, store 8 only needs to be yellow in some arrangements, not all. If, say, store 2 is the one yellow store on the south side instead, store 8 would be red or green, not yellow. So this is not forced either.

Only the claim about store 1 survives no matter how the undetermined stores are filled in, so "red lights decorate store 1" is the statement that must be true.

Let's summarize:

• Store 1's colour is pinned down completely by its neighbour (store 3, forced green) and by the yellow rule (already used by store 5), leaving only red.
• Stores 8 and 10 are never fully pinned down by the base rules alone, since more than one colour remains open for them depending on the rest of the layout.

So the statement that must be true is that red lights decorate store 1.