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.

(In reply to re(2): First Part (spoiler?) by TamTam)

TamTam:

Now that I look at it, Haruki has anticipated us, and ruled out both our solutions.

The problem states:
"You cannot place five coins in a row and count is as two rows of four"

I suspect that any solution is therefore going to involve coins, some of which do not touch.

Posted by Steve Herman on 2006-12-11 17:06:15