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: First Part (spoiler?) by Steve Herman)

The thing is, we're interpreting the question differently. I'm putting the coins together so that the sides touch, and you're not. I figured that was the reason for using coins rather than points in the question.
According to my understanding of the question, the extra diagonals you found in my solution don't count because those coins don't touch each other. Also, your solution wouldn't work, because you wouldn't be able to fit coins 4 and 5 in the middle of the triangle.

Posted by TamTam on 2006-12-11 14:23:55