Count the outcomes
Definition · Level 13 · Interview mechanics
Keep reading with Tradecraft
Without a subscription, you can read three definitions every 30 days. Tradecraft explains all 988 terms and strategies, with the lessons that teach them, flashcards that come back before you forget, quizzes and a payoff lab.
A limit for puzzles about tests: each test has a fixed number of possible results, so t tests give at most (results)t outcomes, and that must be at least the number of cases to separate.
Example
A balance has 3 results: 3 weighings separate 27 cases, 4 separate 81.
Where Tradecraft teaches it
Level 13 · Interview mechanics, in the lesson “Brainteasers: counting and elimination”: Find the answer by counting outcomes, balancing the worst case or ruling options out, and know the classic answers.
Related terms
- 25 horsesFinding the fastest 3 of 25 with five-horse races and no timer takes 7 races: 5 heats, a race of heat winners, then one race for the 5 horses still…
- Bat and ballTogether $1.10, one costs $1 more than the other: the cheap one is 5 cents, not 10 — the classic test of checking your first instinct.
- Powers of 2210 = 1,024 ≈ a thousand; 216 = 65,536; 220 ≈ 1.05 million; 230 ≈ 1.07 billion.
- Trailing zeros of 100!24. Each zero needs a factor 10 = 2 × 5, and fives are the scarce factor: 20 multiples of 5 up to 100, plus 4 extra fives from 25, 50, 75 and 100.
- Twelve-coin weighingOne of 12 coins is heavier or lighter; a balance finds which coin and which way in 3 weighings.
- Two-egg dropWorst-case minimum drops to find the breaking floor of a 100-storey building with two identical eggs: 14 — drop at 14, 27, 39, … so each gap shrinks…