A Single Hit
Ana is a much better shot than Bruno. But once we know that exactly one of them hit the target, comparing their original percentages is no longer enough.
Open riddleChance and uncertainty
Probability riddles
Probability and uncertainty force us to separate intuition from calculation. These random situations reward defining the cases carefully and comparing the available choices.
23 riddlesAll riddles in this topic
After Opening the Envelope
Two envelopes conceal different amounts. Opening one seems to leave you entirely at the mercy of chance, yet that partial information can be used in an unexpected way.
Open riddleFair Ruin
A game of chance can look like a tangle of possible paths. But if the game is fair, there is a way to see it without counting paths: your current money already…
Open riddleSix Loose Ends
Three cords are tied inside a bag without being seen. The outcome feels unpredictable, but there are only fifteen final pairings, and they can be counted exactly.
Open riddleThe Bent Needle
Two needles have the same length. One is straight; the other may be bent at will. Can a clever shape outwit chance?
Open riddleThe broken stick
One stick, two random cuts, three pieces. A simple question to ask whose answer usually surprises.
Open riddleThe Count That Never Turns
Winning an election does not mean having led throughout the count. This puzzle asks for something finer: not just who wins in the end, but how often the lead was never…
Open riddleThe Dice Signature
Two dice can carry different labels and still leave exactly the same fingerprint when their results are added.
Open riddleThe fair coin
One of the minimal gems of randomness: extracting perfect justice from a biased source without knowing the bias.
Open riddleThe Fifteen-Minute Meeting
Two random arrivals, a one hour window, and only fifteen minutes of waiting. The answer is hidden inside a square.
Open riddleThe First-Six Bet
A game can last many rounds, but sometimes it is understood by looking only at the first cycle. If nothing happens at the start, the game returns exactly to where it…
Open riddleThe Jealous Says
Four says, four faces with their own values. At first glance, it seems like a matter of choosing the strongest. But there's something strange about how they relate to…
Open riddleThe Larger of Two Envelopes
Sometimes it seems impossible to improve on a random choice. If you know nothing about two numbers, choosing one of them should give you exactly a 50% chance. This…
Open riddleThe last passenger
A classic probability problem that defies intuition: the answer is the same for any number of passengers, and arriving at it requires looking at the problem from the…
Open riddleThe Lottery Without Enough Randomness
We can choose at random between two options, between a hundred, between a million. But when we want all positive integers to have exactly the same chance, randomness…
Open riddleThe Monty Hall Problem
It seems that, with two doors closed, everything comes down to fifty fifty. However, the odds are not equal: the way the presenter chooses which door to open changes…
Open riddleThe optimal choice
When every rejection is irreversible, choosing well begins with knowing when not to choose. An initial sample can become the standard used for every later decision.
Open riddleThe prisoner and the two urns
An even split seems like the safest choice. Here, however, the best strategy creates one perfect opportunity and concentrates the remaining risk in the other urn.
Open riddleThe Shared Birthday
In a room filled with different dates, a single match is enough. The question is how many people are needed before a match becomes more likely than no match at all.
Open riddleThe Test That Seems Impossible
A test can be very reliable and yet a positive result may not mean what it seems. The mistake is to look only at the test's accuracy and forget how many healthy people…
Open riddleThe urn that reveals itself
Sometimes a single visible piece of information is enough to change the weight of an entire situation. This riddle is deeper than it seems.
Open riddleThree thumbtacks on a plate
There are geometric probability problems where the exact answer emerges from a surprisingly straightforward argument. This is one of them.
Open riddleWhite balls in two boxes
A seemingly simple decision—how to distribute one hundred balls into two boxes—hides a strategy that defies instinct. It's worth stopping before handing out.
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