# Questions tagged [puzzle]

For questions about the mathematical principles behind puzzle, games, riddles, or their possible solutions. Questions that are not strictly mathematical in nature should be asked on Puzzling Stack Exchange.

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### Probability of 3 darts landing in the same half of the board [duplicate]

Problem: Find the probability of 3 randomly thrown darts landing in the same half of the board. More generally, if $n$ points picked uniformly randomly on a disk, find the probability of them lying in ...
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### Creative Algebra Net Problem Solving Question

I came across a problem that I found pretty tedious and difficult to answer and I would appreciate any views or solutions for this question. The diagram shows the net of a cube. On each face there is ...
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### A hypothetical question about probability in a scenario of chicken and clay

I was watching a video on facebook where this chinese merchant sells chicken and clay in a wrappers, the wrappers all looks the same, each bets takes 10 dollars. Assuming that all the customer wanted ...
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### Gear Math Puzzle

The puzzle has 4 gears with 8 ends each, at each end it is randomly labelled with numbers 1-8. The gears are arranged in an 2 by 2 grid and the goal of the puzzle is to match the ends in between each ...
• 1
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### expected value of high-low guessing game

Assume a number between 1-100 (inclusive) is chosen randomly. You then attempt to guess the number. On each guess, if you didn't get the exact number, you're told whether the guess is higher or lower ...
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### Relationship of the Egg Riddle solution to bisection and $\log(N)$ function?

I stumbled upon the video "Can you solve the egg drop riddle? - Yossi Elran" on the TED-Ed YouTube channel. What I found interesting is that in the solution, given that the triangle numbers ...
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1 vote
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### Generation of abstract reasoning puzzles

I'm trying to automatically generate abstract reasoning puzzles. My problem is, that I want to ensure that they "make sense", i.e. there is only one logical correct solution. Suppose, that ...
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### Dividing $N$ coins into at most $K$ groups such that I can get any number of coins by selecting whole groups

Problem Inspired from Dividing $100$ coins into $7$ groups such that I can choose any number of coins by selecting whole groups . I am interested in the number of possible ways we can get such a split....
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1 vote
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### Dividing $100$ coins into $7$ groups such that I can choose any number of coins by selecting whole groups

The problem goes somewhat like this: Let's say that we have 100 coins. Now, I have to split these 100 coins into seven different groups such that I can choose any number of coins only by selecting ...
38 views

### Russian roulette with re-spin intuition for asymmetric solution

Suppose we have a 2-player Russian Roulette game where the barrel is re-spun after every trigger pull. There is 1 bullet in a 6-chamber revolver. Should you choose to be first or second? I am confused ...
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### A 2D circle (cake) is cut randomly with straight lines n-times. What's the expected number of pieces? [duplicate]

This is a Jane Street puzzle, and I will provide my working so far: I defined my 'random' cut as two numbers randomly selected from the range 0-2π mapped to the circumference of the circle, with a ...
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### Which abelian groups and odd integers lead to a well-posed weights puzzle?

Consider the following puzzle (which I quote from here): In a collection of 101 balls, each ball weighs a whole number of pounds. If any one is removed from the collection, the remaining balls can be ...
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### Counterfeit Coins II (green book)

There are 5 bags with 100 coins in each bag. A coin can weigh 9g, 10g, or 11g. Each bag contains coins of equal weight, but we do not know what type of coin each bag contains. You have a digital scale ...
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### Logic Puzzle with truths & lies to questions

Puzzle : We are at a crossroad of 2 paths. One path leads to a swamp and one path leads to the treasure. At the crossroad we meet 2 people , of whom we know that 1 is always telling the truth and 1 is ...
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### Achieving parallel wires with 180-degree rod rotations in an interconnected node system

We have 5 nodes on the left and 5 nodes on the right. You can imagine it this way: the nodes are on parallel rods and are connected with wires so that initially the wires are all parallel. We'll call ...
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### Seeking Book and Online Resource Recommendations for Problem-Solving

I'm looking for recommendations for books or online resources that emphasize problem-solving. While I don't mind if relevant theory is introduced along the way, I'm not looking for materials that ...
1 vote
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### Generous Banker

You are at the bank and it is your lucky day. The banker is going pick random positive integer and you are too. You are both allowed to determine the probability distribution on the positive integers ...
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1 vote
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### Game - two players take turn moving a marker to an adjacent square in a 9x9 grid

A marker is placed in the centre of a $9$x$9$ grid. Ann and Beth take turns moving the marker to one of the adjacent squares (one sharing a side) provided that this square has never been occupied by a ...
63 views

### Minimum number of weighings

Akbar has four golden crowns that he can wear. He does not know their exact weight but knows that all of them are an integral number of grams. Birbal has a balance that displays the difference of ...
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1 vote
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### Given 99 bags of red and blue sweets, is there a selection of 50 bags containing at least half of each type of sweet?

Assume you have 99 bags containing sweets of two kinds, say blue and red. Is it always possible to pick out 50 bags such that you have at least half the total of red sweets and half the total of blue ...
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1 vote
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### How can i find the way to escape robot?

A scout robot is trapped at the center of a square with side length 1km. The scout robot can move at a speed of 3km/h. A guard robot is located at a vertex of the square, and patrols the boundary of ...
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### A long-form mathematics books tetris questions

I am currently trying to solve the problem 1.4 from the book Proofs: A long-form mathematics textbook. This problem is about tetris, and it requires to prove that it is impossible to cover a 4x5 chess ...
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1 vote
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### Simple solution to random walk

The final score of a football match was 4:3 in favour of the home team. How many ways could the result have gone if there was a period of the match when the away team was leading? I have learnt of a ...
1 vote
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### Expected payout riddle: How to keep signature collectors from forging?

I made up this riddle, but I don't know how to solve it. Marissa owns a company that collects signatures. Marissa can only hire perfectly rational self-interested agents (as defined in game theory), ...
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1 vote