1.  (a) Prove that every tree has at least two nodes of degree 1.
	(``Using what you know about the sum of the degrees.'')

    (b) Using part (a) and ordinary induction, prove that every tree
	can be colored with two colors.


2.  (Induction:)  Show the vertices of a certain graph can be 3-colored.
	(Graph is triangles recursively inscribed inside each other--
	a1, a2, a3 is outer triangle A
	b1, b2, b3 is inside; b's are midpoints of sides of A
	c1, c2, c3 is inside; c's are midpoints of sides of B...

3.  (Induction:)  Prove that any graph with 2n nodes and no 3-cycles
	has at most n^2 edges.
	(In inductive step, remove two adjacent vertices so at most
	 1+2n edges are removed.)

4.  (Strong induction:)  Prove that every integer can be written as a product
	of primes.

5.  (No induction, but don't tell!:)  Prove that G can be colored with 
	k colors if every vertex has degree less than k.

	Multiple parts?:
	First define Greedy alg. for coloring a graph
	Use Greedy:
	(warm-up: 0.  show ordering of (the 8) vertices of the 3-cube s.t.
			Greedy requires 4 colors; 3 colors; 2 colors.)
	1.  there is an ordering of the vertices of any graph s.t.
		Greedy does optimally.
	2.  to prove thm. above (color G with k colors if...)
	3.  to prove thm with degrees less than *or equal* to k
		if some vertex has degree less than k and G is connected.
		(Order the vertices properly for greedy.)

6.  Binary algorithm for GCD, not declared as such--just give code, 
	ask them to recognize it.

	1.  Ask for the arguments passed to each recursive call on 	
		a few particular inputs, like 28 & 42, etc.
		that is, for them to step through the algorithm
	2.  Ask for conjecture on the function computed, and proof?