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 could be an accurate list of the colours of the lights that decorate stores 2, 4, 6, 8 and 10, respectively?

• A. Green, red, green, red, green
• B. Green, red, green, yellow, red
• C. Green, red, yellow, red, green
• D. Yellow, green, red, green, red

Hint:

Work out store 3 and store 6 first since their colour is forced by both a same-side neighbour and the store facing them, then use those fixed colours to test the four lists.

Answer 1

The Correct Option is B

Step 1: Set up the street and mark what is fixed.
The north side, west to east, is stores 1, 3, 5, 7, 9. The south side, west to east, is stores 2, 4, 6, 8, 10. Store 1 faces store 2, store 3 faces store 4, and so on down to store 9 facing store 10. We are told store 4 is red and store 5 is yellow, and every store is green, red, or yellow, with no store sharing a colour with its same-side neighbour or with the store it faces.

Step 2: Fix store 3.
Store 3 faces store 4 (red), so store 3 cannot be red. Store 3 also sits next to store 5 (yellow), so store 3 cannot be yellow either. The only colour left for store 3 is green.

Step 3: Fix store 6.
Store 6 sits next to store 4 (red), so store 6 cannot be red. Store 6 faces store 5 (yellow), so store 6 cannot be yellow. That leaves green for store 6 as well.

Step 4: Fix store 1.
Rule 3 says yellow lights decorate exactly one store on each side, and on the north side that store is already store 5. So stores 1, 3, 7, and 9 cannot be yellow. Store 1 sits next to store 3 (green), so store 1 cannot be green either. With yellow and green both ruled out, store 1 must be red.

Step 5: Test the four remaining lists against these fixed colours.
We now know store 4 is red and store 6 is green for certain, no matter what. Option 1 (green, red, green, red, green) gives no yellow at all on the south side, but rule 3 needs exactly one yellow store there too, so option 1 fails that rule. Option 3 (green, red, yellow, red, green) puts yellow at store 6, but we just showed store 6 has to be green, so option 3 is wrong. Option 4 (yellow, green, red, green, red) puts store 4 at green and store 6 at red, but store 4 must be red and store 6 must be green, so option 4 breaks two fixed facts at once.

Step 6: Confirm option 2 works.
Option 2 reads store 2 green, store 4 red, store 6 green, store 8 yellow, store 10 red. Check the chain along the south side: green next to red is fine, red next to green is fine, green next to yellow is fine, yellow next to red is fine, so no two neighbours clash. Check the facing pairs: store 1 (red) faces store 2 (green), store 3 (green) faces store 4 (red), store 5 (yellow) faces store 6 (green), and each pairing differs. Store 8 being the one yellow store on the south side also satisfies rule 3. Everything holds together, so this list is a possible arrangement.

Final Answer:
Only option 2 (green, red, green, yellow, red) can be the actual colours of stores 2, 4, 6, 8, and 10. \[ \boxed{\text{Option 2}} \]