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 coin.

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.

PART 1
Now, how many coins are needed to make as many rows of 3 as there are coins?

PART 2
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
     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