House Number Logic
A red, blue, green, and yellow house are all on the same side of a street that travels west to east, in that order.
The westmost house has the smallest house number and the numbers get larger for each successive house, although the numbers are not necessarily in some arithmetic pattern. The numbers correspond to distance, so (for example) house numbers that are 4 apart are twice as far away as house numbers that are 2 apart.
Based on the clues below, what is the yellow house numbered?
1.) All the houses have even numbers.
2.) The green house is further from the blue house than it is from the yellow.
3.) The red house is 10 apart from the yellow house.
4.) The blue house is #242. The three distances from the blue house to the other houses are all different numbers.
The answer is 250.
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1 solution
We know green is closer to yellow than blue. Since the differences are even, green is at least 2 from yellow and at least 4 from blue. Since red and yellow are ten apart, ther are 2 possibilities: blue is 4 from red and 6 from yellow, or blue is 2 from red and 8 from yellow.
If blue is 4 from red, than it will also be 4 from green, since it is the minimum of 6 from yellow. This violates the fourth condition, so we know yellow and blue are 8 apart. Since yellow also has the highest number, we conclude that its number is 2 4 2 + 8 = 2 5 0