Starting an the origin on an infinite grid, you follow a predetermined path going up (U), down (D), left (L), or right (R). You paint every square you visit, including the square you started at and the square you finish at. Using this method, we can paint the number six using the instructions RRD...

Move the Knight! Your knight is on (0, 0) on an infinite (to all of the four edges, not just two) chessboard, and you need to move it to (a, b). You can use arbitrary (but finite) number of moves to do that. Since the chessboard is infinite, you can use squares with negative coordinates. Since yo...

Say you have an infinite 6 by 6 grid, now say you want to cut a rectangle with dimensions LxW out of it such that the overhang, i.e., the distance from any vertex up to the cut line less than 6, is less than or equal to 1.5. The output will be the left, right, up, down over hang distance. Boom! O...

A positive integer \$x\$ is an \$n\$-perfect number if \$\sigma(x) = nx\$, where \$\sigma(x)\$ is the divisor sum function. For example, \$120\$ is a \$3\$-perfect number because its divisors sum to \$360\$: $$360 = 3\times120 = 1+2+3+4+5+6+8+10+12+15+20+24+30+40+60+120$$ and $$926073336514623897...

Background Tetris is a single-player game played on a rectangular grid with tetromino pieces. When you fill one or more lines with tetrominoes, the filled lines are removed, and all blocks above them move down accordingly. In the following diagrams, . is an empty space, # is an existing block, an...