savoy082

Pt En In today's post I will be sharing a game I made with just under $400$ lines in Processing, a wrapper for Java that makes drawing to the screen really easy. The goal of the game is really simple: go from the cell you are standing on (marked with the black outline of the ellipse, in the screenshot) to the cell that is framed in white. To do that, you can move a "cursor" (the black frame) with the $AWSD$ keys to choose the next cell you want to go to. To move, press the space bar. There are a couple of rules to moving, though: You can only move to the selected cell if it is in the same row or same column as the cell you are in; You can only move to the selected cell if it has the same colour or the same shape as the cell you are in. Rule number $1$ says you can only go in the directions these orange arrows cover: Rule number $2$ says that, from the cells specified by the above rule, you can only go to the white circle, diamond or vertical ellipse (precisely becau...

[ Link to code, you can try it in the end of the post] Suppose you have an infinite source of water and two buckets of capacities $5$L and $3$L. Through juggling around the water in the buckets, can you find a way to have one of the buckets hold exactly $1$L of water? A possible way of doing it would be: Fill the bucket of $3$L and then pour its water into the $5$L one; Fill the bucket of $3$L. At this point you have $3$L in each bucket; Pour the bucket of $3$L into the $5$L one. Since the bigger one already had $3$L in it, only $2$ will fit, meaning there will be a remaining litre in the $3$L bucket. I find this problem a very interesting one, and it is not hard to generalize it: given $N$ buckets of capacities $c_1, c_2, \cdots, c_N$, as well as a target value $T$ and an infinite source of water, is there a sequence of moves that puts exactly $T$ litres in one of the buckets? There are some cases for which one can immediately say that there is no such sequence. On one hand, if $T ...