How many coins are needed to make as many rows of one coin as there are coins? The answer is 1: you make 1
row of one coin using that 1
How many coins are needed for rows of two coins? The answer is 3: put the coins in a triangle and you make 3 rows of two coins using 3 coins.
Now, how many coins are needed to make as many rows of 3 as there are coins?
If that was easy, how many for 4?
Note: if you are making rows of 4, any line drawn can intersect with a maximum of 4 coins. (you cannot place 5 coins in row and count it as two rows of 4) And no stacking coins.
Basically, I drew three nested pentagrams (five-pointed stars).
This drawing starts with a large pentagram (10 points, 5 rows). I drew another smaller pentagram inside the inner pentagon (5 more points, 5 more rows). Then I drew one last pentagram, even smaller inside the second (5 more points, 5 more rows). The last 5 rows are drawn from each of the 5 points of the largest pentagram through the center.
The following drawing is only two nested pentagrams, but hopefully, you get the picture.
o o o o
o o o o
Perhaps there's a better answer out there.
Posted by Tristan
on 2006-12-12 13:29:22