# 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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### Probability of a similar sub-sequence of length X in two sequences of length Y and Z

Say we have two random sequences of length $y=3300$ and length $z=26$, where the sequences are made out of a combination of $k=4$ four letters ACGT. the letter in each position of the sequence is ...
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12 views

### Calculate and calibrate speed of processing products

I want to define a metric -for a factory worker- with respect to how fast she/he is processing products. Assuming that she/he has to process 5 items and the time between those items is dt1, dt2, dt3, ...
• 159
1 vote
78 views

### (Open-ended?) Stat puzzle about expected value

A fair coin is flipped $200$ times and each time it lands on heads, $1$ dollar is added to a pot. After this process is over, an auction is held for the pot. There is exactly one other person at the ...
• 153
83 views

### Measuring sticks to minimize error

I encountered the following problem while preparing for an interview: There are two sticks $A$ and $B$ with different lengths. In addition, you are given a ruler. However, the ruler is not perfect: ...
188 views

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 ...
• 143
1 vote
34 views

### Stats Puzzle About Random Guesses [closed]

If you are told to guess a number between 1 and 100 that is as close as possible to the standard deviation of the guesses of others who are told the same thing, what number would you guess?
206 views

### Normal Distribution Puzzle/Riddle

Some time in the future, a lottery takes place, with winning number N. 3 of your friends from the future, John, Joe, and James, provide you with guesses on the number N. John's guess a is randomly ...
1k views

### 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 ...
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6k views

### 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. ...
• 506
263 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 ...
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 ...
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2k 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 (...
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### 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 ...
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3k 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
134 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 ...
125 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, ...
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665 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 ...
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1 vote
219 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 ...
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49 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 <...
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1 vote
86 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 ...
• 45
89 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 ...
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231 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 ...
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1 vote
119 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 ...
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86 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?
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. ...
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6k 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 ...
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