How could I learn the Rust programming language in about a week, and by the end of the week make a meaningful project were I show what I have learned. Tell me examples of projects I could make and what I should be learning first as a intermediate programmer who knows the basics.
Learning a new programming language in a week is a challenging task, but it is possible if you can dedicate a significant amount of time and effort each day. Here are some tips and resources to help you learn Rust and create a meaningful project in a week:

1. Start with the Rust Book: The Rust Book is the official documentation for Rust and provides a comprehensive guide to learning the language. It covers everything from basic syntax to advanced topics like ownership and lifetimes. As an intermediate programmer, you may want to skip some of the basics, but it's still a good idea to review the fundamentals to ensure that you have a solid understanding of the language.

2. Work through Rust by Example: Rust by Example is another great resource for learning Rust. It provides a series of hands-on examples that cover a wide range of Rust features and concepts. You can work through these examples to get a feel for the language and practice your coding skills.

3. Explore the Rust Standard Library: Rust has a rich standard library that includes modules for common tasks like networking, file I/O, and collections. You can explore the standard library to get a sense of what Rust has to offer and how you can use it to build powerful applications.

4. Choose a Meaningful Project: When choosing a project, it's important to choose something that you're interested in and that will challenge you. Some possible project ideas for Rust might include building a command-line utility, creating a web application using a Rust web framework, or working on a system-level project that interacts with the operating system.

5. Look for Examples and Tutorials: As you work on your project, don't hesitate to look for examples and tutorials that can help you along the way. There are many resources available online, including the Rust documentation, Stack Overflow, and various Rust blogs and forums.

Here are a few project ideas that you might consider:

- Build a simple chat application that uses Rust and websockets.
- Create a command-line tool that converts Markdown to HTML.
- Implement a basic file synchronization tool that uses the rsync algorithm.
- Write a Rust wrapper for a C library that you're interested in.

To get started with your project, you should begin by reviewing the Rust Book and Rust by Example to get a solid understanding of the language. From there, you can start exploring the Rust Standard Library and other Rust resources to find the tools and libraries that you need for your project. Finally, don't forget to leverage the Rust community and online resources to help you learn and grow as a Rust programmer. Good luck!
How would I get started on the 3rd idea, the project synchronisation algorithm?
Good choice. 

Assuming that you want to create an example program, and not a `rsync` client that is compatible with existing clients, you can follow this simplified plan:

1. Read about the theory behind `rsync` algorithm, for example, at https://www.cs.tufts.edu/~nr/rsync.html 
2. Write the module that computes the per-block fingerprint, in rust, and demonstrate to yourself that it works, by writing tests on a fixed data.
3. Write the module that computes the fingerprint for all blocks on a given file. Make sure that it works well by writing an automated test on an example data.
4. Read about one of the common networking protocols, e.g. ZeroMQ, from https://zguide.zeromq.org/docs/chapter1/
5. Write an example client and server, where the client can connect to the server and send an example message. Demonstrate to yourself that it works by writing a script that will start the server, start the client, have the client to connect to the server and send a message, and finally, shut down the client and server.
6. Extend the client with the modules written previously, so that the message sent are the `rsync` file fingerprints, rather than the example message. At this point, it will be enough to test that the message received by the server is the same that has been sent by the client. 
7. Extend the server to compute the fingerprints on the file that it has, AND compare it with the fingerprints received from the client. 

This is not a complete plan, but from here on the plan should be simple to continue: write a small additional bit of functionality, and add a test. 

Please let me know if you need help with more steps or with any of the particular steps.