Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [puzzle]

Use this tag for statistical puzzles that challenge the ingenuity of the solver. (Do not use the tag "games" for this purpose.)

Reference: http://en.wikipedia.org/wiki/Puzzle

Puzzles are often contrived as a form of entertainment, but they can also stem from serious mathematical or logical problems.

28 questions
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15 answers

The Monty Hall Problem - where does our intuition fail us?

From Wikipedia : Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another…
Rizwan Kassim
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Did Statistics.com publish the wrong answer?

Statistics.com published a problem of the week: The rate of residential insurance fraud is 10% (one out of ten claims is fraudulent). A consultant has proposed a machine learning system to review claims and classify them as fraud or no-fraud. The…
ChrisG
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7 answers

Two envelope problem revisited

I was thinking of this problem. http://en.wikipedia.org/wiki/Two_envelopes_problem I believe the solution and I think I understand it, but if I take the following approach I'm completely confused. Problem 1: I will offer you the following game. You…
evan54
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The frog problem with negative steps

Standard Problem description In this question The Frog Problem (puzzle in YouTube video) a frog has to jump from leaf to leaf on a row of leaves. And the question is how long it takes on average to reach the end. In that specific case the frog only…
Sextus Empiricus
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11
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6 answers

Statistics library with knapsack constraint

Suppose you had $200 US to build a (very) small library of statistics books. What would your choices be? You may assume free shipping from Amazon, and any freely available texts from the internet are fair game, but assume a 5 cent charge per page to…
shabbychef
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11
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1 answer

Will there ever be an unhappy Tribble in Oz?

Here's an amusing problem brought to me by a student. Although it was originally phrased in terms of mutually annihilating bullets fired at regular intervals by a gun, I thought you might enjoy a more peaceable presentation. In the infinite flat…
whuber
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9
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Modified sleeping beauty paradox

Consider the following classic problem: Some researchers would like to put Sleeping Beauty to sleep on Sunday. Depending on the secret toss of a fair coin, they will briefly awaken her either once on Monday (Heads) or twice (first on Monday then…
user514014
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4 answers

The Frog Problem (puzzle in YouTube video)

There is an interesting puzzle in YouTube video Can you solve The Frog Problem?. I'll try to give an equivalent formulation here. A frog is on one side of the pond and wants to get on the other side. There are $n$ lily leaves ahead in a line, the…
polettix
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need intuition: why is there no winning strategy to this game?

I have 1000 cards on the table, R1 are red and B1 are blue. You have 1000 tokens on the table, R2 are red and B2 are blue. Each turn, you get to pick a token, and I randomly choose a card with uniform distribution. If they have the same color, you…
ihadanny
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How to solve Chuck-a-Luck puzzle

Story (spoilers!) The puzzle: Chuck-a-Luck is a gambling game often played at carnivals and gambling houses. A player may bet on any one of the numbers 1,2,3,4,5,6. Three dice are rolled. If the player's number appears on one, two, or three …
greenoldman
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Value iteration does not converge when using Q learning

I have a simple game and want my agent to play it with a help of reinforcement learning. We have a board and a value in each cell. The goal is to go from start to finish point with the highest score (agent can go in 4 available directions: up, down,…
Most Wanted
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Probability of having 2 girls and probability of having at least one girl

In this question the general formula P(A|B) = P(A ∩ B)/P(B) is used. I understand through intuition why the answer should be 1/3. What I don't understand is why P(both girls, at least one girl) is 1/4. I know that P(A ∩ B) = P(A)P(B) if A and B are…
Tharuka Devendra
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Uniform random variables and optimal strategy

This comes from Fivethirtyeight's riddler weekly challenge... Toddler poker is played by two players. Each is dealt a “card,” which is actually a number randomly chosen uniformly from the interval [0,1]. (It could be 0.1, or 0.9234781, or 1/π,…
Demetri Pananos
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Puzzles using Kolmogorov's zero–one law

Do we have any interesting puzzles/problems using Kolmogorov's zero-one law? Maybe a classic brain teaser or problems like those in Fifty Challenging Problems in Probability?
Kenneth Chen
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Old race car problem/puzzle

This was in an old (1935) "brain teaser" book, and I can't figure it out how to solve it! There's a car race during which the cars experience 4 different types of car trouble, e.g. flat tire, blown motor, etc. I can't recall exactly what they are…
Ramblin Wreck
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