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.

9 coins do it as follows:

                 1

             2  3   4
               5   6
          7     8      9

Where the lines are 127, 789, 149 (the three outside lines),
    234, 258, 468 (three inside lines) and 138, 269, 457.

Posted by Steve Herman on 2006-12-14 12:20:34