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.

Uncertain if this is optimal for PART 1:

I can make 9 (or 10) rows of 3 using 9 coins.

1     2     3

   4  5  6

7     8     9

{(1,2,3), (1,4,8), (1,5,9), (2,4,7), (2,5,8), (2,6,9), (3,5,7), (3,6,8), (4,5,6), (7,8,9)}

If only 9 rows are allowed then

1     2     3

   4  5     6

7     8     9

eliminating (2,6,9) and (3,6,8) and adding (3,6,9).

Posted by Leming on 2006-12-11 13:04:04