Tag Logic Puzzles

Classic logic puzzles in which you infer or deduce actions and outcomes based on information provided

Logical List Puzzle

Which logical statement(s) below must be correct?

  1. Exactly one statement on this list is incorrect
  2. Exactly two statements on this list are incorrect
  3. Exactly three statements on this list are incorrect
  4. Exactly four statements on this list are incorrect
  5. Exactly five statements on this list are incorrect
  6. Exactly six statements on this list are incorrect
  7. Exactly seven statements on this list are incorrect
  8. Exactly eight statements on this list are incorrect
  9. Exactly nine statements on this list are incorrect
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Majority Vote Puzzle

After the results of an election, you are told that one candidate has received the majority of the votes, but you don’t know which candidate. You have exactly one opportunity to hear the votes, but:

  • The list of votes is very long
  • The votes will be announced one after another in random order
  • You have a poor memory (can only remember a couple of names or numbers)
  • You are not allowed to write or record anything

Given these restrictions, is there a way figure out which candidate received the majority of votes?

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Tennis Match Mystery

Abe, Ben, and Catelyn were playing 1-on-1 tennis matches one afternoon. After each match, the winner stayed on the court and the loser was replaced by the person who sat out.

At the end of their session, Abe had played 8 matches, Ben had played 12 matches, and Catelyn had played 14 matches. Ben was particularly exhausted as he had played all of the last 7 matches.

Is it possible to figure out who played and who won in the 4th match?

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Deducing Bicycle Spokes

A bicycle shop has some unique bicycles. Each bike is identical, and each bike’s front and back wheels has at least one spoke each. You don’t know how many bicycles are in the shop, but you know there are between 200 and 300 spokes in total.

If you knew the exact number of spokes, you would be able to figure out the number of bicycles.

You don’t know the exact number of spokes, but just knowing the fact that you would be able to figure it out with that information allows you to deduce the answer. How many bicycles and spokes are there?

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5 Pirates Puzzle

Five pirates are figuring out how to divide up a newly plundered treasure of 100 gold coins. From most senior to least senior: Pirate A, Pirate B, Pirate C, Pirate D, and Pirate E. The rules:

  1. The most senior pirate must propose a distribution (for example, giving himself all 100 gold coins and 0 for everyone else), and then all the pirates must vote on it.
  2. If at least half of the pirates vote for a proposal, the proposal is accepted and the gold is split according to that distribution.
  3. Otherwise, if the proposal is rejected, the pirate that proposed it is kicked out, and this process repeats with the remaining pirates.
  4. Each pirate’s main goal is to maximize the gold they receive (but a pirate that is kicked out gets no gold), but are also spiteful enough to prefer kicking out the other pirates, all else equal. The pirates are also distrustful of each other and will not make any side deals, so the distribution of an accepted proposal is final.

What is the greatest number of coins that Pirate A can distribute to himself?

This is a classic logic puzzle, occasionally encountered in tech interviews many years ago.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

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Rigging a Vote

There are five candidates participating in an unusual election. There are four rounds of voting, and only two candidates participate in each round, with the winner moving on and the loser dropping out. This means first candidate 1 will run against candidate 2, then the winner will run against candidate 3, and so on, with the winner of the last round being elected.

Polling shows that Stephen Hawking is not very popular. There are five equal-sized groups in the voting population, and polling shows they prefer the candidates in the following order:

  • Group 1: Einstein > Newton > Maxwell > Hawking > Curie
  • Group 2: Newton > Curie > Maxwell > Einstein > Hawking
  • Group 3: Curie > Maxwell > Einstein > Newton > Hawking
  • Group 4: Einstein > Newton > Hawking > Curie > Maxwell
  • Group 5: Newton > Maxwell > Einstein > Hawking > Curie

But Hawking has a secret weapon – he gets to choose the order the candidates participate in each round.

Is there a way for Hawking to organize the rounds such that he wins?

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Island of Blue Eyes

There is an island known for its people with blue eyes, yet there is at least one green-eyed person on the island. No one knows the color of their own eyes, as there are no reflective surfaces on the island and discussion of eye color is forbidden, but they can see everyone else’s eye color. If any islander were to come to know that they do not have blue eyes, they would leave the island in shame before the next sunrise.

One day, an outsider visits the island and remarked how there was at least one islander with green eyes. Within the day, every islander had heard and understood this new information.

Assuming departures from the island are noticed by everyone by the next day, and assuming each islander is highly logical and is able to keep track of all other islanders’ eye colors and actions – what happens to the islanders and does it depend on the number of green-eyed islanders?

This is a classic logic puzzle, also known under a different story (but same core logic) as Josephine’s Problem.

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Boxes of Apples and Oranges

There are three identical boxes of apples and oranges, except one contains all apples, one contains all oranges, and one contains a mix.

The boxes are labeled “apples”, “oranges”, and “apples and oranges” but all 3 boxes were labeled incorrectly!

You have the opportunity to inspect fruit from the boxes one at a time, without looking inside the box. What is the fewest number of fruit you need to inspect to correctly label the contents of the identical boxes?

This was a popular brainteaser in some engineering interviews a while back, including a software quality assurance engineer interview at Apple.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

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