Binary image
Your task it to write a simple program to decode some arrays of data into a black-and-write graphic.
The graphic is composed of n lines of black and white pixels. We use . to represent a white pixel; O to represent a black pixel.
For example, here is one line of graphic
....OOO.
We s...
The travelling sales man problem
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?"
In this puzzle not nec...
Zhiwei Sun Squares
Given a positive integer n, find the number of ordered tuples (a, b, c, d, e) over non-negative integers for which a² + b² + c² + d² = n and b + 3c + 5d = e².
Note: A conjecture by 孙智伟 (Sūn, Zhìwěi) states that this count is always at least 1.
For example, if n is 9, there are ...
Brain**** interpreter
Brainfuck is a minimalist programming language consisting of 8 commands. That's all.
However it is Turing complete and allows you to make whatever you want, if you are very patient and motivated.
Your goal is to create a fully functional Brainfuck interpreter.
Let see how it...
Knights jam
The knight is a chess piece that, when placed on the o-marked square, can move to any of the x-marked squares (as long as they are inside the board):
.x.x.
x...x
..o..
x...x
.x.x.
Eight knights, numbered from 1 to 8, have been placed on a 3×3 board, leaving one single square empty .....
Let's define a grouping as a flat list, which is either:
just 0
2 groupings followed by the literal integer 2
3 groupings followed by 3
4 groupings followed by 4
etc. (for all integers \$ \ge 2 \$)
Note that 1 is not included in this definition, because otherwise groupings could be infinite.
Fo...
