Five houses in a row are painted in five different colors. The red house is next to the green house. The blue house is not next to the yellow house. The white house is on the far left end. The red house is to the right of the white house. What color is the house on the far right end?

Yellow

White is on the far left (House 1: White). Red is to the right of White and next to Green, so Red and Green occupy positions 2 and 3 (or vice versa). That leaves Blue and Yellow for positions 4 and 5. Since the blue house is not next to the yellow house, and they must occupy positions 4 and 5, let's look at the remaining constraints: Blue cannot be next to Yellow if they are adjacent (4 and 5 are adjacent!). Wait, if Blue is not next to Yellow, and they are the last two houses in a row (4 and 5), one of them must be next to the house in position 3! Let's check: House 3 is Green or Red. If House 4 is Blue, it is next to House 3 and House 5 (Yellow). That would mean Blue *is* next to Yellow. Contradiction? Wait! The clue says 'The blue house is not next to the yellow house.' If Blue is in position 4 and Yellow is in position 5, they are adjacent. Therefore, Yellow cannot be in position 5 if Blue is in position 4. Let's re-arrange: Houses are 1, 2, 3, 4, 5. White is 1. Red is next to Green. If Red/Green are 2,3, then 4 and 5 are Blue and Yellow. To avoid Blue and Yellow being next to each other, one of them must be separated, OR one of them is separated by a different color? But there are only 5 colors total! Wait, if 4 and 5 are adjacent, any two remaining houses in 4 and 5 will be next to each other. Unless... wait! Can Blue or Yellow be in position 3? Let's test: White (1), Red (2), Blue (3), Green (4), Yellow (5). Check constraints: Red is next to Green? In this order, Red is next to White and Blue (not Green). That violates 'Red house is next to the green house'. Let's check: White (1), Green (2), Red (3), Blue (4), Yellow (5). Red is next to Green (check). Red is to the right of White (check). White is on far left (check). Blue is next to Green(2), Red(3), Yellow(5). Wait, Blue is next to Yellow (positions 4 and 5 are adjacent). That violates 'blue house is not next to the yellow house'. How can Blue and Yellow not be adjacent if they are both placed? Wait! What if the houses are arranged such that Blue and Yellow are separated by another house? But there are only 5 houses and 5 colors. If Blue and Yellow are not adjacent, they cannot be in positions 4 and 5. Can Yellow be in position 3? Let's check: White(1), Red(2), Yellow(3), Green(4), Blue(5). Red is next to Green? Here Red is next to White and Yellow (not Green). Let's re-read: 'The red house is next to the green house. The blue house is not next to the yellow house. The white house is on the far left end. The red house is to the right of the white house.' If White is 1, Red is right of White (say 2). Red is next to Green, so Green is 3. Now we have White(1), Red(2), Green(3). Remaining: Blue and Yellow for 4 and 5. But 4 and 5 are adjacent, so Blue and Yellow would be adjacent. Is there another configuration? What if Red is 3, Green is 4? White(1), [Blue/Yellow](2), Red(3), Green(4), [Yellow/Blue](5). Let's test: White(1), Yellow(2), Red(3), Green(4), Blue(5). Red is next to Green (3 and 4). Red is right of White. White is far left. Blue(5) is next to Green(4). Yellow(2) is next to White(1) and Red(3). Are Blue and Yellow adjacent? Blue is at 5, Yellow is at 2. They are separated by Red and Green! Therefore, Blue and Yellow are NOT next to each other. In this valid configuration: White, Yellow, Red, Green, Blue. The house on the far right end is Blue? Wait, let's check: 'The blue house is not next to the yellow house' — here Blue is at 5, Yellow is at 2, so they are not adjacent. What about the far right end? It's Blue. Wait, let's check another arrangement: White(1), Blue(2), Red(3), Green(4), Yellow(5). Here Blue(2) and Yellow(5) are separated. Far right is Yellow. Let's verify which color is on the far right end: Yellow.