Invariants and Monovariants in Dynamical Systems
Read this topicExplanations 4
- Invariants (Part 1) Invariant is something that doesn't change after some operation. This is a very useful technique in maths, and we'll see a few applications of invariants. Ex…
By Zi Song Yeoh
- Invariants (Part 2) Parity This is a nice problem that demonstrate the power of parity. Let a1,a2,...,ana_1, a_2, ..., a_na1,a2,...,an represent an arbitary permutation of th…
By Zi Song Yeoh, Alex Federspiel
- Invariants (Part 3) Monovariants Monovariants are values that is either nondecreasing all the time or nonincreasing all the time. A simple example of a monovariant is this : Gre…
By Zi Song Yeoh, Alex Federspiel
- Invariants are, typically, things that stay invariant (don't change) during a process. Here's an example. Here's another example, where there's not really a process, but we can …
By Victor Wang
Problems 4
- There are 202020 geese numbered 1−201-201−20 standing in a line. The even numbered geese are standing at the front in the order 2,4,…,202,4,\dots,202,4,…,20, where 222 is at the…
- David has a collection of 40 rocks, 30 stones, 20 minerals and 10 gemstones. An operation consists of removing three objects, no two of the same type. What is the maximum number…
- There are 25 ants on a number line; five at each of the coordinates 111, 222, 333, 444, and 555. Each minute, one ant moves from its current position to a position one unit away…
- You have a 2 x 3 rectangular chocolate bar, that you want to eat one square at a time. What is the fewest amount of splittings you would need to break the bar completely into it…