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Problem Sets

The finite bank — open-ended teasers and book/competition problems, grouped by method. Reveal, self-grade, and work a method to mastery. (Looking for the advanced "explain" concepts? They moved to Concepts.)

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Start here — your weakest methods

Pigeonhole: when collision is unavoidable
☆☆☆☆☆ Level 0
Not started · 87 cards · tutorial
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Invariants: the quantity the move can't touch
☆☆☆☆☆ Level 0
Not started · 75 cards · tutorial
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Recursion: relate the big problem to a smaller copy
☆☆☆☆☆ Level 0
Not started · 71 cards · tutorial
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Counting & Pigeonhole · 4 methods

Pigeonhole: when collision is unavoidable
☆☆☆☆☆ Level 0
Not started · 87 cards · tutorial
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Complement: when 'not the thing' is easier
☆☆☆☆☆ Level 0
Not started · 70 cards · tutorial
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Extremal principle: lean on the most extreme element
☆☆☆☆☆ Level 0
Not started · 64 cards · tutorial
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Inclusion-exclusion: fix the over-counting by alternating
☆☆☆☆☆ Level 0
Not started · 13 cards · tutorial
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Parity, Invariants & Coloring · 4 methods

Invariants: the quantity the move can't touch
☆☆☆☆☆ Level 0
Not started · 75 cards · tutorial
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Coloring: when 2 colors aren't enough — escalate to ≥3
☆☆☆☆☆ Level 0
Not started · 61 cards · tutorial
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Parity: when a 2-coloring decides the question
☆☆☆☆☆ Level 0
Not started · 46 cards · tutorial
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Symmetry: when relabeling does the counting for you
☆☆☆☆☆ Level 0
Not started · 40 cards · tutorial
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Recursion & States · 5 methods

Recursion: relate the big problem to a smaller copy
☆☆☆☆☆ Level 0
Not started · 71 cards · tutorial
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Optimal stopping: the threshold rule
☆☆☆☆☆ Level 0
Not started · 10 cards · tutorial
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First-step analysis: condition on the first transition
☆☆☆☆☆ Level 0
Not started · 9 cards · tutorial
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Backwards induction: solve from the terminal state
☆☆☆☆☆ Level 0
Not started · 8 cards · tutorial
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Dynamic programming: memoize the overlapping subproblems
☆☆☆☆☆ Level 0
Not started · 7 cards · tutorial
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Probability Core · 4 methods

Conditional probability: shrinking the sample space
☆☆☆☆☆ Level 0
Not started · 45 cards · tutorial
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Law of total probability: average over the hidden case
☆☆☆☆☆ Level 0
Not started · 14 cards · tutorial
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Geometric probability: probability as a ratio of areas
☆☆☆☆☆ Level 0
Not started · 14 cards · tutorial
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Bayes' rule: inverting the conditioning
☆☆☆☆☆ Level 0
Not started · 11 cards · tutorial
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Expectation & Linearity · 2 methods

Linearity of expectation: decompose, then sum
☆☆☆☆☆ Level 0
Not started · 28 cards · tutorial
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Indicator random variables: choose the indexing first
☆☆☆☆☆ Level 0
Not started · 14 cards · tutorial
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Markets & Arbitrage · 1 methods

Arbitrage: when prices have to agree, or you get paid
☆☆☆☆☆ Level 0
Not started · 13 cards · tutorial
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