COMBO PLATES
A. There are 27 possible combination plates. If, for example, you start with a yellow item, you then have a choice of three different red shapes for the second and three different green shapes for the third (3 x 3 x 3 = 27).
B. There 84 possible different combinations. For the first item you can choose any one of nine items. Since all items in the plate must be different, that leaves eight choices for the second item and seven for the third, for a total of 504 combinations (9 x 8 x 7 = 504). But as there are six different ways to arrange any group of three items, many of the 504 plates have the same items, just in a different order. To find the number of different combinations, divide 504 by 6, which gives 84 combinations.
C. There are 81 possible combination plates. The only combinations excluded are those that have only one shape. There are 3 such combinations, each containing all three colors. That leaves 81 combinations (84 – 3).
D. There are 36 possible combination plates. There are three possible color pairings and three possible shape pairings, for a total of 9 (3 x 3) possible combinations of two colors and two shapes. For each such combination there are four possible items to choose from (two colors and two shapes), and there are just four ways to choose three items from a set of four. So the total number of combination plates is 36 (9 x 4 = 36).
E. There are 6 possible combination plates. For the first color you have three choices of shape. For the second color there are two remaining choices of shape. For the third and last color you must choose the one leftover shape (3 x 2 x 1 = 6).
DOMINO PIZZAZZ
This puzzle was adapted from my mobile phone game, Daily Puzzle, published by Sorrent (www.sorrent.com). The answers below are grouped to show the number of vertical rectangles in each solution.
A. The paired vertical rectangles form squares.
B.
C.
FIDDLE FIGURES
This puzzle was also adapted from my mobile phone game, Daily Puzzle.
A. There are 20 possible figures. There are six possible positions for the lines and 20 ways to form groups of three out of these six elements.
B. There are 32 possible figures. All have a vertical or horizontal line, a curve running across the diagonal, and a diagonal line. There are four possible positions for the vertical or horizontal line, four for the curve, and two for the diagonal (4 x 4 x 2 = 32).
C. There are 24 figures. All have a horizontal or vertical line and two diagonal lines (which can create one diagonal). There are six positions for the diagonal lines and four for the horizontal or vertical line (6 x 4 = 24).
