Classic Logic Puzzles (Weighing, Crossing, Hats)

Product and consulting interviews use classic logic puzzles to test structured reasoning under pressure. You're not expected to have memorised the answer — you're expected to reason aloud, test cases, and converge logically. Knowing the famous templates gives you a huge head start.

The classic families

Puzzle	Key insight
8 balls, 1 heavier, a balance	Split into 3 groups → 2 weighings (log₃, not halving)
Bridge crossing (torch, times)	Send the two slowest together; fastest ferries the torch
Prisoners & hats	Back person counts parity (odd/even) of a colour
Poison bottles / 1000 bottles	Binary-encode bottles across testers (10 testers → 1024)

Exam Tricks & Tips

• 🎯 For weighing puzzles, divide into THREE groups, not two — a balance gives 3 outcomes, so think log base 3.
• 🎯 Think in bits for identification puzzles — n testers/trials distinguish 2ⁿ items (poison bottles, coins).
• 🎯 Reason out loud and test small cases — interviewers score the approach, not instant recall.
• 🎯 For hats/prisoners, use parity — the first speaker encodes the count of a colour as odd/even.
• 🎯 State your strategy before computing — "I'll minimise worst-case weighings" shows structure.
• ❌ Common mistake: blurting a remembered answer with no reasoning — if the interviewer tweaks the numbers, you're stuck.

Expected pattern: Common in product/consulting/quant interviews; usually one puzzle you must reason through aloud.

Quick recap: Weighing → three groups (log₃); identification → binary/bits (2ⁿ); hats → parity. Reason aloud, test cases, state strategy first.

Cover the answer, recall, then check. 10 cards on classic logic puzzles.

Q1. How many weighings to find 1 heavy ball among 8?
A1. Two — split into three groups (3-3-2) because a balance gives three outcomes (think log₃).

Q2. Why three groups, not two, in weighing puzzles?
A2. A balance has three outcomes (left, right, equal), so base-3 thinking is optimal, not halving.

Q3. Bridge-crossing key insight?
A3. Send the two slowest together and have the fastest ferry the torch back.

Q4. How many testers to find 1 poison among 1000 bottles?
A4. Ten — binary-encode bottles across testers; 2¹⁰ = 1024 ≥ 1000.

Q5. General rule for identification puzzles?
A5. n testers/trials distinguish 2ⁿ items — think in bits.

Q6. Hats/prisoners puzzle technique?
A6. The first speaker encodes the parity (odd/even count) of a colour so others deduce theirs.

Q7. What do interviewers actually score on puzzles?
A7. The reasoning approach and case-testing, not instant recall of the answer.

Q8. Why state your strategy before computing?
A8. It shows structure — e.g., "I'll minimise the worst-case number of weighings."

Q9. Common puzzle mistake?
A9. Blurting a memorised answer with no reasoning — you're stuck if numbers change.

Q10. First move when stuck on a puzzle?
A10. Reason out loud and test a smaller version of the problem.

Product and consulting interviews love classic logic puzzles — weighing coins on a balance, getting people across a bridge, prisoners guessing hat colours. They rarely test knowledge; they test how you reason out loud under uncertainty. The good news: the famous puzzles recur, and each family has a repeatable technique. Learn the techniques and the specific puzzles, and you'll handle most of what's thrown at you.

What this covers / why it matters: the recurring puzzle families (weighing, river-crossing, hats) with their core techniques and fully worked classics. It's about method and composure as much as the answer.

The approach

Beginner — the universal puzzle method

Whatever the puzzle, follow the same steps out loud:

1. Restate the problem and constraints precisely (interviewers often hide a key detail).
2. Start with a simpler / smaller case to find the pattern.
3. Think in terms of information: each weighing/question should split the possibilities as evenly as possible.
4. Narrate your reasoning — a wrong path explained beats a silent right answer.

Intermediate — the weighing technique

On a balance scale, each weighing has three outcomes (left heavier, right heavier, balanced), so n weighings distinguish up to 3^n cases. To find one odd item, divide the group into three roughly equal parts and compare two of them — this is the ternary-search idea and it's the key to almost every weighing puzzle.

Advanced — crossing and hat techniques

• River/bridge crossing: the constraint is usually a limited carrier (a torch, a boat) that must return, and the total time/trips is dominated by the slowest members — send the two slowest together, and use a fast person as the ferry, to minimise the cost.
• Hat puzzles: the trick is almost always parity/counting or using what others do/say as information. One prisoner encodes a global fact (e.g. the parity of red hats), letting everyone else deduce their own.

Worked example

Weighing — "9 coins, one is heavier, find it in 2 weighings on a balance."
"Split 9 into three groups of 3. Weighing 1: put group A (3 coins) vs group B (3 coins). If they balance, the heavy coin is in group C; if A is heavier, it's in A; if B is heavier, it's in B. Either way I've narrowed it to 3 coins in one weighing. Weighing 2: take those 3 coins, weigh one vs one. If they balance, it's the third coin; otherwise it's the heavier side. Found in 2 weighings. The idea generalises: with the 3-outcome balance, 2 weighings cover up to 3^2 = 9 coins."

Bridge crossing — "4 people, one torch, cross a bridge in the dark; only 2 can cross at a time and they move at the slower person's pace. Times: 1, 2, 5, 10 minutes. Minimum total?"
"The key insight is to not let the two slowest (5 and 10) cross separately — send them together, and use the fastest (1) as the torch ferry. Optimal: 1 and 2 cross (2 min), 1 returns (1), 5 and 10 cross together (10), 2 returns (2), 1 and 2 cross (2). Total = 2 + 1 + 10 + 2 + 2 = 17 minutes. Crossing the 10 and 5 together is what beats the naive 'fast person shuttles everyone' answer of 19."

What interviewers look for

• A clear method — you don't guess randomly.
• Information-efficient thinking — each step maximally narrows possibilities.
• Constant narration — they follow your reasoning.
• Composure — you stay calm and structured when stuck.

Do's and don'ts

• Do restate constraints and try a smaller case first.
• Do think in outcomes/information (a balance gives three outcomes).
• Don't blurt a memorised answer with no reasoning — they want the process.
• Don't go silent; narrate even dead ends.
• Mnemonic: RISE — Restate, Info-split each step, Simplify to a small case, Explain aloud.

Worked Example

Problem/Question: You have 8 identical-looking balls; one is slightly heavier. Using a balance scale only twice, find the heavy ball.
Solution/Model answer: The trick is to divide into three groups, since each weighing has three outcomes (left heavier, right heavier, balanced).
Weighing 1: Split into groups of 3, 3, and 2. Put the two groups of 3 on the scale.

• Case A — they balance: the heavy ball is in the group of 2. Weighing 2: weigh those 2 against each other; the heavier side is the ball. Done.
• Case B — one side of 3 is heavier: the heavy ball is among those 3. Weighing 2: take that group of 3, weigh 1 vs 1.
  • If one is heavier, that's the ball.
  • If they balance, it's the third (un-weighed) ball.
    Either way, exactly two weighings identify the heavy ball.
    Answer/Takeaway: Split 8 balls into 3-3-2 and weigh the two 3s. If they balance, the odd ball is in the 2 (weigh them). If not, it's in the heavier 3 (weigh 1 vs 1, the balance implying the third). The key insight: a balance gives three outcomes, so divide into thirds, not halves.