Sample		Proof		Machinery	Example
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finite		cases		Tree diagram	Intransitive dice
finite		game		Tree diagram	Monty Hall
uncountable	inf sums	Tree diagram	HTH beats HHH
parameterized	induction	basic		Covering a square with L-shaped tiles
param				expectation	Pennies-on-edge trick
finite		bijection			red-black ``stop'' card game
finite		game/cases			Which hand has the higher number?
param				approx/counting	Birthday paradox
param				expectation	coupon collector
param				approx/counting	Love machine
finite				expectation	Chuck-a-Luck
param				expect/tails/	random vs. nonrandom sequences
				counting/Boole/
				asymptotic
finite		induction	equiv/st.mach.	Die Hard 2
finite		pigeonhole	case		three friends or strangers among six people
finite		pigeonhole			hairs on head
param		incl/excl			Derangements
uncountable	cases		tree		Triangular Duel
finite		cases		counting	Mind-reading trick
param		induction	harmonic	book stacking
uncountable			recurrences	gamblers ruin	
param				cond.prob./	Jenga (Herb Simon)
				geom.sums./
				Wald
param		induction	harmonic	Desert Storm
param		induction	recurrences	Tower of Hanoi
param		induction			red/black pairs card trick
param				tails		countdown card trick
finite		case				extract cube roots
param		induction	base rep/	binary number cards
param				Chebychev	jellybeans?


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Game theory - Many games
Linear Recurrences - Paper cutting with Fibonacci numbers