It is a common pasttime to try to arrange things in lines. Gardeners find it pleasing to arrange trees in patterns that line up at various points.
Mathematicians wonder about things like, given 9 trees or coins or dots, what is the most number of lines of three you can make. As a start, we know we can get 8 lines this way:
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Puzzle 1: Arrange 9 pennies on a table, in such a way that there are 10 different lines of 3 pennies each.
Puzzle 2: If you have 10 pennies, can you arrange them in 5 rows of 4?
Puzzle 3: If you have 16 pennies, how many different lines of 4 can you achieve?
I give up, show me the solution.