Problem number 28. Some birds, including ha, long, nha, and trang, are perched on four parallel wires. There are 10 birds perched above ha. There are 25 birds perched above long. There are 5 birds perched below nha. There are 2 birds perched below trang. The number of birds perched above trang is a multiple of the number of birds perched below her. How many birds in total are perched on the four wires? This problem involves a lot of trial and error, so we will present one solution that tries to avoid this. We will use a couple of logical steps, but there might be steps that are skipped, just to make the solution not too long. In context, when you're trying to solve this problem, you might want to be organized and try all possible variations for this problem. But in this case, we will just present one solution that works. There are a few steps you can use to get started. For example, we know trang cannot be on the bottom wire, because there are some birds below her. We also know nha is above trang, since there are more birds below nha than trang, and there are actually 3 birds between them, one of whom is trang herself. Using this, we can start to figure out how these birds are perched on the wires. We know that there are only 2 birds below trang, and since 2 is not that many compared to the other numbers in the problem, we see a 25, which is pretty large. We can maybe safely assume that trang has to be on the third wire. Trang can't be on the bottom wire, but if trang is higher up, then that means that there are very few birds on all the wires below. So trang will go on the third wire, and nha will go above trang, just because there are not too many birds between them. This means that there are 3 birds on the wire trang is on, and there are 2 birds on the wire that's below trang. Now, we can start to fill out the rest of the diagram. There are 25 birds perched above long. So that means that long should probably be on the bottom wire, because we know that the 25 is by far the largest number in this problem. It makes sense for long to be on the bottom most wire, and there not to be too many birds below long. If we try this out, then we'll see that there should be 25 birds in this range, enclosed by the braces. Let's put ha on the second wire. The reason being that if ha is on the third wire, then there should only be 10 birds above ha. But that means that we already know how many birds are on the third wire, 3, and that wouldn't add up to 25. The only way we can get 25, since we know ha still has to be placed, is for ha to be on the second wire. This means that there are 10 birds on the first wire, and there are 25 birds, as before, on the top 3 wires. So this wire has to have 12 birds. Now, we can start to check the conditions. There are 10 birds above ha, that's correct. There are 25 birds above long, that's right. There are 5 birds below nha, that's right. There are 2 birds below trang, that's right. And the number of birds above trang is a multiple of the number of birds below her. Well, there are 22 birds above trang, and 2 birds below her, so that's also right. This means that this configuration works. Let's count the total number of birds. There are 25 in the top 3 wires, and 2 in the bottom, so the total number of birds is 27. And that means that the answer is a, 27.

birds arrangement

logical deductions

wire constraints

bird configuration

total birds