Batch 2 - Class 305 - Robert Abbott's Mazes

• A clown was juggling five equal triangular pieces of cardboard, each a right-angled triangle with 1 inch base and 2 inch height. He then proceeded to cut one of them, and claimed that he could make a perfect square by reassembling the 6 pieces. Can you do the same?
• Answer:

• Mazes are essentially state diagrams. Traffic maze is a multi-state diagram, in the sense that your next state(s) dont just depend on your position, but also on the direction you are coming from.
• You can think of these as graph traversals. But the nodes are not just positions, but multi-states of position and direction you are coming from. Lets try and draw this for the traffic maze.
• Note that if you are coming back to a multi-state in a particular path, that is unnecessary repetition
• You can apply graph search algorithms like depth-first-search or breadth-first-search to mazes
• Sometimes it helps to solve the maze from result backward - some combination of start-out and finish-in approaches can help narrow down the options a lot. Lets apply this to some of the mazes and see where we get to
• Traffic Maze:  There are certain roads that you have to travel first in one direction then later in the opposite direction. The trick is finding a way to get yourself turned around. The rules say that U-turns are not allowed. But there are loops, if you can find them, that you can follow to get turned around. (Solution https://www.logicmazes.com/solucity.html)
• Three Dot Maze:  Most of the tricky part of this maze happens at the beginning. Notice the two blocks that are shaded in this diagram. You must begin the maze by repeatedly looping around those two blocks until you can travel through the yellow dot at the upper-left heading north. (Solution https://logicmazes.com/soludot.html)

• Mrs. Smith and Mrs. Jones had equal number of apples but Mrs. Jones had larger fruits and was selling hers at the rate of two for a penny, while Mrs. Smith sold three of hers for a penny. Mrs. Smith was for some reason called away and asked Mrs. Jones to dispose of her stock. Upon accepting the responsibility of disposing her friend's stock, Mrs. Jones mixed them together and sold them of at the rate of five apples for two pence. When Mrs. Smith returned the next day the apples had all been disposed of, but when they came to divide the proceeds they found that they were just seven pence short, and it is this shortage in the apple or financial market which has disturbed the mathematical equilibrium for such a long period. Supposing that they divided the money equally, each taking one-half, the problem is to tell just how much money Mrs. Jones lost by the unfortunate partnership?
• Answer: 21 pence