(a) compute the sums of the squares of rows 1-4 of pascal's triangle. that is, compute:
$$\binom10^2 + \binom11^2$$
$$\binom20^2 + \binom21^2 + \binom22^2$$
$$\binom30^2 + \binom31^2 + \binom32^2 + \binom33^2$$
$$\binom40^2 + \binom41^2 + \binom42^2 + \binom43^2 + \binom44^2$$
do these sums appear anywhere else in pascal's triangle?

(b) guess at an identity based on your observations from part (a). your identity should be of the form
$$\binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 = \text{ something}.$$
(you have to figure out what "something" is.) test your identity for $n=1,2,3,4$ using your results from part (a).

(c) prove your identity using a committee-forming argument.

(d) prove your identity using a block-walking argument.