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.

    1
  
  2   3 4
    5
6   7   8
  9
  0

Supposed to be 1, 6 and 8 forming an equilateral triangle with 5 at the center, 2,3 and 7 at the midpoints of the sides. 
This has 10 points and 10 lines of 3:{(126)(138)(234)(258)(356)(678)(479)(370)(290)(157)}
It has no lines of 4 or more.

Edited on December 12, 2006, 10:45 am

Posted by Jer on 2006-12-12 10:41:22