GROUP DYNAMICS
COMBO PLATES
Illustration by Lee Krasnow
A display plate shows the nine à la carte items on the menu of the trendy Combinatorial Café. Each day of the week, the café challenges diners to create their own three-item combination plates based on a special theme.
A [Easy] Monday’s panchromatic plate is any three items of three different colors. How many different combinations are possible?
B [Challenging] Thursday’s binary plate is any three items that include just two colors and two shapes. How many combination plates are possible?
C [Challenging] Wednesday’s metamorphic plate is any three items that include at least two different shapes. How many different plates are possible?
D [Challenging] Tuesday’s triadic plate is any three different items. How many different combination plates are possible?
E [Challenging] Friday’s mix-master plate is any three items, no two of which are the same color or the same shape. How many different plates are possible?
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DOMINO PIZZAZZ
How many ways are there to fit six dominoes together to make each of the forms at right? One solution is shown for each form. Hint: Find a systematic way to count all the combinations for each box. For instance, possible configurations for form A can include zero, two, four, or six vertical dominoes.
FIDDLE FIGURES
In each panel below, the figures are constructed from one set of geometric elements, and these elements appear in all their possible positions. But the figures shown are only a sampling of the different ways those elements can be combined. How many different figures can be made from each set of elements? Hint: First determine what the figures in each group have in common. For example, every figure in panel A contains exactly three lines.
A
C
