The prototypical example of a finite field is for a prime number.  We can also construct fields with elements by analogy with the complex numbers.  Choose a non-square and define to be the set of all formal expressions of the…

In the puzzles, jumps are allowed on both lines, but they can’t overlap. At the final rabbit-sequence doodle at the end of the game, they allow jumps on every line and they can be bracket nested so and [()] is…

one domain is computability, which studies what can be computed, and how in a rather abstract sense: largely what is described in Suresh Venkat’s answer. another is algorithmics, that finds effective means to compute answers to specific problems, with specific…

1. 3 6 13 27 55 111 … All of these types of problems can be answered by a simple polynomial fit: y=1720∗(−n6+39∗n5−325∗n4+1425∗n3−2194∗n2+2496∗n+720) < p easy if you think about it first ten elements would be: 1,3,6,13,27,55,111,218,409,727,1224

Alice and Bob are perfectly logical and super intellegent. Their professor decides to play a game with them, and he tells them: “I have chosen two numbers x and y with 2≤y≤x≤100. I will tell Alice the value of their…

just some enigmatic partitions of the chemical elements I have partitioned the chemical elements into two groups based on a certain property that is shared by some of them, but not by the remaining ones. The following elements have my enigmatic…

How I solved the Gear Cube Extreme Solve the middle layer Solve the corners 2.1 Resolve middle layer parity and centers (if there is a problem) Move the edges to the correct layers Move the edges into the correct positions Rotate…