Brain Teasers and Puzzles

Brain teasers, puzzles, riddles, and other challenges

Card Flipping Endgame

There are n playing cards lined up face-down in a row. Every turn, a pair of adjacent cards with the left card face-down is randomly selected (i.e., a pair of cards has no chance of being selected if the left card is face-up, otherwise all pairs are equally likely to be selected). Both cards are then flipped over (face-down to face-up or face-up to face-down).

Prove that after enough turns, it will eventually be impossible to select a pair of cards with the left card face-down.

When you reach this card flipping endgame, will the rightmost card be face-up or face-down?

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Drink Mix Riddle

Two kids are playing around with their drinks at lunch. One has 200ml of milk and the other has 200ml of chocolate milk. They scoop 20ml of chocolate milk into the milk glass, then they scoop 20ml of whatever is in the milk glass into the chocolate milk glass.

When they’re done, is there more chocolate milk in the milk glass or more milk in the chocolate milk glass?

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Number Deduction

A teacher gives three clever students in her class a challenge: she writes down 3 different numbers on 3 index cards, and has each student hold up one of the cards to their forehead such that they can’t see their own card but everyone else can.

She tells them each card has a different number, and that two of the numbers add up to the third number, and asks them to figure out their number without sharing the numbers they see.

Ava sees Sid has 40 on his forehead and Vlad has 60 on his forehead.

Ava says “I don’t know my number.”

Vlad says “I don’t know my number.”

Before Sid can say anything, Ava realizes she is now able to figure our her number! What is Ava’s number?

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Tricky, Tricky

Can you figure out the number I am thinking of?

Some cryptic clues:

  • Call it sin, and mess it up (9)
  • Between θ and κ (4)
  • Engage emotionally (5)
  • Half a byte (6)
  • Mottle (5)
  • Never mix meds & gin (7)
  • – (4)

If you have all the answers right, that’s only about 33% percent of the solution: you need to justify them too.

Some clues were left over, so here’s a second set:

  • Sing about the matter (10)
  • Frog’s pole (3)
  • Heroin or slap (5)
  • 0 or 1 (1,3)
  • A toy asking a question on an online forum (4+2 = 6)

An ingenious and very difficult puzzle by Bass on Puzzling StackExchange (spoiler warning: contains the solution)

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