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.)

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3
votes
1answer
200 views

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 ...
28
votes
2answers
4k views

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 ...
4
votes
2answers
265 views

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 (...
2
votes
1answer
54 views

Fraction / Percentages Brainteaser

In my business math class, the instructor put up the following case study, and asked us to find any flaws in the logic, but, I have been unable to see what is wrong with the following argument: "A ...
4
votes
2answers
2k views

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....
1
vote
1answer
99 views

Expected payoff vs. payout for expected outcome

Someone pointed out this puzzle in Kahneman's Thinking, Fast and Slow. I paraphrase. A game rewards participants based on how long it takes to obtain the first heads in a toss of a fair coin. If ...
5
votes
1answer
94 views

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, ...
2
votes
1answer
157 views

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 ...
1
vote
1answer
125 views

Probability puzzle solved by R simulation; answer close but not exactly. Bug in my code? [closed]

Here's an interesting probablity puzzle: One hundred people line up to board an airplane. Each has a boarding pass with assigned seat. However, the first person to board has lost his boarding ...
0
votes
0answers
38 views

Maximize the difference of the means of two sets

I have a set of real numbers which I'll call set A. I have a threshold t. I have sets B and <...
1
vote
1answer
72 views

Optimal strategy for a simple game

Let's say I'm playing a game that works likes this: I have n bowls that are each filled with a different number of marbles, and I know how many marbles are in each bowl. At each round, the dealer goes ...
2
votes
0answers
77 views

Modified German Tank problem involving string distance metrics

Pretend we have a list of items, e.g. names, and we know it is sorted ALPHANUMERICALLY let's say in ascending order. Given a small set of the first K items, how can we estimate the length of the full ...
12
votes
1answer
170 views

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 ...
1
vote
1answer
87 views

Ticket selling probability puzzle

I was talking with a friend of mine about a simple statistical puzzle that we weren't able to solve due to our ignorance about the statistics world. Consider a ticket selling web. A musical event is ...
4
votes
0answers
67 views

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?
16
votes
7answers
5k views

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. ...
3
votes
1answer
3k views

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 ...
11
votes
6answers
484 views

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 ...
40
votes
13answers
5k views

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 ...