Fighting with computers

Java Network Programming uses the DatagramPacket class as the data representation for UDP datagrams. Whether you want to send or receive it, it will be a DatagramPacket . In a recent exam, we asked our students to create a simple UDP echo server.   The logic of such a server is that it waits endlessly until it receives a UDP datagram and then sends it back to the same address (IP and port number) from which it came. Nothing complicated, but the devil is in the details, and some students wrote a program that would create a new DatagramPacket for each datagram received. It is not wrong, as it works, but it is a bit wasteful, as it places more stress on memory allocation and garbage collection than needed.  However, I was surprised when chatGPT commented on the code I got from DeepSeek-R1 as a sample solution, where a call to setLength() was made after each iteration. It did not make sense to me, but chatGPT went on for quite a while, reasoning why it was needed. Eventually...

QUESTION: I f the center of a hexagon is located at a (0,0) coordinate, which are the coordinates of each vertex if the length of the side of the hexagon is 10 mm? Analyzing and reasoning phase Okay, so the user wants to find the coordinates of each vertex of a hexagon centered at (0,0) with a side length of 10 mm. Let me think about how to approach this. First, I remember that a regular hexagon can be inscribed in a circle. Each vertex is equally spaced around the circumference. The key here is relating the side length to the radius of the circumscribed circle. Wait, is the radius the same as the side length? Hmm, no, I think that's only true for a hexagon with a side length equal to the radius. Wait, actually, in a regular hexagon, the side length is equal to the radius of the circumscribed circle. Let me confirm that. In a regular hexagon, all sides are equal, and all internal angles are 120 degrees. The radius of the circumscribed circle (distance from center to a vertex) is ...