DIAL “P” FOR PUZZLE
These days a typical cell phone not only functions as a means of communication but also as a portable entertainment center equipped with a miniature game console. The games below are adapted from a cell-phone series I’ve developed called the Daily Puzzle.
Shape Shifters
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ONE [Easy] How many squares of any size can you find in this figure? To get you started, one square in the figure has been shaded green.
TWO [Challenging] How many triangles of any size are in this figure? One triangle has been shaded blue.
THREE [Difficult] How many trapezoids are in this figure? A trapezoid has four sides, only two of which are parallel. One trapezoid here is shaded purple. The others must have the same proportions as the shaded one but may be any size and in any orientation. Mirror images are allowed.
Dot Matrix
Imagine that the nine grids below are printed on nine separate transparent squares of plastic. If you were to stack up some of the plastic sheets, you could create many different patterns of dots.
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1. [Easy] Which two grids could you superimpose to make the following pattern? (Grids may not be rotated.)
2. [Challenging] Which three grids can be superimposed to put a dot in every square? (Grids may not be rotated.)
3. [Challenging] Which six grids could you superimpose to place exactly two dots in every square? (Again, grids may not be rotated.)
Stick Kin
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1. [Easy] Which figure has five cousins?
2. [Challenging] Arrange all nine figures in a sequence so that each figure is a cousin of the next. Which figures are the first and the last in the sequence?
3. [Challenging] Two figures are second cousins if one figure can be turned into the other by moving just two sticks to new positions. Which figure is a cousin or second cousin of all the other figures? Hint: Note that no sticks in Figure 1 touch the center, and four sticks in Figure 4 touch the center.
