## Math Maze

Math Maze can be found in Dell Math Puzzles And Logic Problems. I wrote to them asking for permission to use one of their puzzles as an example, and never heard from them. So here is a simple puzzle of my own.

The puzzle is a grid, with numbers at the left and top. You are supposed to draw a meandering line (path) to traverse the maze, from the entrance arrow to the exit arrow. This line will go from square to square, horizontally or vertically, never diagonally. The numbers tell how many squares, either to the right of the number, or below the number, that your path will cross. Your path cannot cross itself. It can only enter and exit a square once. If your path enters a square in one direction, it must exit through one of the other three sides. Your path cannot go outside the grid.

In this particular puzzle, we have a row and a column labeled 5. Our path must go through all of those squares, so we can mark them with a dot (a handy symbol, as we can later connect dots). We have identified all two of the squares to the right of the "2," so we can mark the rest with an X, and draw part of the path. We have identified all four squares in the column marked with the "4." On the right we see how I have marked this diagram, so far. To continue, we have identified all three of the squares in the second row, and all two squares of the fourth column, and can mark four more X's and more of the path. The rest of the puzzle is easy.

Besides reasoning, some trial and error may be appropriate.

Here are a few more clues. In the diagram on the right, a+b+c+d=m+n+o+p. That sum is just the number of squares that the path goes through. And here, a+b+c+d is odd. If one path is odd, then all paths are odd. These two clues can sometimes help, when there are shortcuts and barriers.

Here we have a column with a number of 1 (the middle column). First of all, this column must be entered from the left, and exited to the right. Also, if a+b is even, then the path goes through an x. If a+b is odd, then the path goes through a y. If the one-column were one square to the left or right, then the opposite would be true: if a+... is even, then the path would go through a y. And if the one-path goes through row o (as in the diagram), then o is at least 3.

Another clue is that if a path goes through a corner square, then it also goes through the two adjacent squares (except where the path begins or ends). Yet another clue is that a path cannot cross itself. In the diagram on the right, the path that I have drawn is impossible, as it would have to cross itself somewhere.

Here are two more puzzles which I designed: