275. The Pen Puzzle. Answers to well-known puzzles given in old books are often completely wrong. Nevertheless, it seems that no one ever notices these errors. Here is one such example.

A farmer had a pen with a fence that was 50 rails long, in which only 100 sheep could fit. Suppose the farmer wanted to expand the pen so that it could hold twice as many sheep.

How many additional rails would the farmer need?
275. The old answer is that if you arrange the poles as shown in case \(A\), then by adding two poles at each end, as in case \(B\), you will get double the area. It should be noted that, firstly, the problem does not specify the shape of the enclosure. Secondly, even if it were required that the original enclosure had dimensions of \(24 \times 1\), the answer would still be incorrect, because if you arrange the poles as in case \(C\), the area will increase from 24 "square poles" to 156, and the enclosure will hold 650 sheep, with the number of poles remaining the same. Moreover, you can double the area as in case \(D\), using only 28 poles. If it is required to use all the poles and double the area exactly, you can do so as shown in case \(E\).

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-239.jpg?height=677&width=596&top_left_y=324&top_left_x=730)