Intense Logic

I guess I'm writing this because I want to reflect on what's going on while taking the logic course. Just finished the Multi-Level thinking chapter and I think that the hardest part was, by a mile and a half, the hat color with many people section. I can't believe that level of difficulty exists. Here's what I've learned:

Ask the right questions.
Know that others will know and predict what they'll do accordingly.
If your strategy gives you an answer of the sort "impossible to tell" then maybe its not the right strategy.
Relationships among objects (I call them elements when it comes to strategy) is key. In some hat color problems, the elements are hat colors and numbers. How can we use them to guarantee knowledge?
Some strategies will give the answer naturally, even by convenience (the "let's see what happens" strategy)
Patience my friend. Patience.

My main concern is how to progress to that. I failed that quiz. I think it was incredibly hard. One way to do it is to do a bunch of practice problems but I want to finish the relevant courses first (so that I can get the most out of it). With that said, logic is gonna be my main concern. Another way, and this I do not know how to start, is to create my own problems. Are there any suggestions on how to start?

I'm calling this note "Intense Logic" not because it is intense for everyone but because it is intense for me. Perhaps I can use the following path: Logic --> Joy of Problem Solving (I guess I need pre-requisites) --> Computer Science. How do you conclude notes? Thanks!

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`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
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Comments

If you want to write your own problems, you could

take an existing problem and think further or change some parts of this problem.
make a geometry problem where you can construct some lines, triangles, circles or whatever you want and then ask for some angle, length, or so.
make a logic problem, for example some statements, of which some are false, and then we have to find something out (who's the murder? where's the gold? ...)
let you inspire by a real-life problem, like paying money, finding the shortest route, ...

I hope this helps a little bit. If you have any questions, just ask me!

Henry U - 2 years, 4 months ago

I wrote my first one. It's easy to solve but it's something. https://brilliant.org/problems/humans-and-werewolves-part1/

Jay B - 2 years, 4 months ago

It's a good problem, considering it's your first one! I also like the way you presented the question, it was very clear what you wanted. Well done!

@Henry U – Thank you! to be honest I kind of got lucky. I just started writing sentences and then added the restriction. It happened to work on the first try. I guess that's how it works for these type of problems. Write sentences, add restrictions and see what happens. Modify if needed. Thanks for your reply.

Dude, I looked at your profile and you're super smart and you're 16! Nice to make your acquaintance. I'm trying out a bunch of courses and can't seem to keep up so I decided to force myself into a single topic for the moment (well, primarily because I'm taking science stuff too). I chose logic. Hopefully I can get good and perhaps co-op a logic/number theory problem. That ought to be nice. It's a goal at least.

Logic is a good first topic, as most of the other courses require logical thinking (cases, ...). When you understand logic, you'll have a good foundation for other topics and will improve there. I'm sure you'll reach your goal!

I think you'll like this one https://brilliant.org/problems/saving-ice-cubes-base-43/

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$