CUNY Math Challenge

I've registered for 4 Rounds of fun. Because I also want some money $2,500.

First round questions: (One week left)

Problem 1
How many different (non-congruent) triangles have integer side lengths and perimeter 2014?

Alcuin's Sequence is the hint. A detailed explanation. Thanks to JM.
Problem 2
You have 2014 identical looking coins and a two-pan balance scale with no weights. One of the coins is fake, but you do not know whether it is lighter or heavier than the genuine coins, which all weigh the same.
Describe a procedure to determine in the minimum number of weighings whether the fake coin is lighter or heavier than the others.

Pile them in 3s or 2s. Looks like all these can be googled.
Problem 3
A fair coin is tossed repeatedly until 3 heads appear consecutively. On average, how many times is it tossed?

This is kindergarten level.
Problem 4
There are four knights on a 3 3 chessboard: two white knights at the bottom two corners, and two black knights at the two upper corners. Show how to switch the knights in the minimum number of moves so that the white knights are at the upper corners and the black knights are the bottom corners. (Knights cannot land on each others squares during this process.)

I need a board. But this is supposed to have been solved: Guarini's Problem