MAY'S PUZZLE: RECTANGLES IN A SQUARE


On a piece of paper, imagine a square that has gridlines and 4 columns and 4 rows, as Figure A shows.

How many different rectangles drawn on the gridlines can you identify within the square (including the outer lines forming the 4×4 square)?

SOLUTION TO APRIL'S DOTS ON A CUBE PUZZLE


In April's puzzle, there were two dots marked arbitrarily on the surface of a cube. You were asked to define the shortest path connecting the two dots on the cube's surface.

A recommended way to solve the problem is to start from the simplest case—the two dots are marked on the same side—then try to apply that logic to the more complex cases. Obviously, a straight line is the shortest path connecting two dots marked on the same side of the cube. To apply the same logic to the more complex cases in which the dots are marked on different sides, you need to visualize the cube's surface as a plane by unfolding and spreading the adjacent sides. After you have a flat surface, the shortest path between the dots is still the straight line connecting them.

There are multiple ways in which you can spread the surface to generate a plane. The purpose of the puzzle was to identify the logical key, which was spreading the sides of the cube to generate a flat surface and drawing a straight line between the dots. So, you don't really need to define which of the different spreads gives you the shortest straight line. Suffice it to say that the shortest path between the two dots is the shortest straight line out of the different spreads that you can generate.