Questions tagged [puzzle]

Question 1

We flip a coin $n$ times. The probability of tails is $p$. Let $X$ be the number of occurrences of a run of heads followed by a longer run of tails. We can also agree that if the sequence begins with ...

Question 2

Two players, $A$ and $B$, play the following game. Player $A$ chooses an integer $x$ between $1$ and $10$. Then, starting with player $B$, the players take turns adding to $x$ any integer between $1$ ...

Question 3

Let $R_{m,n}$ be an $m$x$n$ rectangle where $m$ is the width and $n$ is the length, and $R_{m,n}$ is subdivided into a grid of unit squares. A line segment is a horizontal or vertical segment drawn ...

Question 4

For clarification, s sets of all asymmetric n-ominoes means s copies of each of the k asymmetric n-ominoes. Non-trivial means that for $n = 5$, you can’t take the F, L, P, N, Y pentominoes and do this ...

Question 5

If the wording of the question was a little confusing, here is the main idea: Some $n$-ominoes cannot tile rectangles. We are excluding those. Excluding those $n$-ominoes not tiling any rectangle, ...

Question 6

Some context and motivation for this question: A friend posed to me the following puzzle. Given eight points in the unit disc, why must there exist a pair of points with distance less than $ 1 $? The ...

Question 7

For any $n$, what's the minimum number of sets needed for all free $n$-ominoes to be able to be tiled in a rectangle? For $n = 1$ and $n = 2$ the answer is 1 as there is only one monomino and domino. ...

Question 8

I just read this riddle which i find quite interesting: Two friends are staying at the same hotel. While chatting in the lobby, one says to the other: "The difference between the least common ...

Question 9

Finding solution of a Sliding Puzzle of size $N \times N$. asks about solving a sliding-block puzzle with multiple holes. Apparently a 2-hole puzzle is always solvable; as those who've played with the ...

Question 10

I believe context will help before the statement of the problem. I was asked In the picture below, can you find a closed, non-intersecting loop visiting every white square exactly once? (If you do, ...

Question 11

In 1981, Kontsevich proposed the following problem. Imagine a chessboard that extends infinitely in only two directions: upwards and to the right. Put one pebble in each colored cell of the figure (...

Question 12

I am exporting slides to pdf at an Optoma interactive touchscreen display I use in my lectures. The order of pages in the exported pdf is shuffled and I am trying to understand the logic how the ...

Question 13

I am looking for some probability problems in which there is a symmetry that you don't notice in the first place, but by noticing it, you can easily get the answer. I have two examples in mind, and in ...

Question 14

Happy September 27th, 2025! A good friend of mine, let's call him Bob, wrote to me today with an interesting tidbit. Write Sept. 27th, 2025 in Month-Day-Year notation to get 09/27/2025. If you remove ...

Question 15

I am working with a physical puzzle consisting of 32 unique pieces. Each piece can only connect to certain other pieces, and all pieces must be connected together into one single assembly. There are ...

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Questions tagged [puzzle]

In the limit, what probability of tails maximizes the expected number of shorter runs of heads followed by a longer run of tails.

how to win the $100$ game?

What is the minimum number of line segments required to split a rectangle into the 12 free pentominoes?

What's the minimum number of sets in which you can tile all asymmetric n-ominoes into a non-trivial symmetric shape?

What is the smallest rectangle tileable by copies of each n-omino that can tile a rectangle?

Can the unit disc be covered by seven squares, each of area one-half?

What's the minimum number of sets of n-ominoes needed for it to able to be tiled into a rectangle?

A riddle involving the difference between lcm and GCD

Generalized sliding-block puzzle

Minimum # of black squares to guarantee uniqueness of loop visiting all white squares

Adapted Kontsevich "Pebbling a Chessboard" game: can you win it?

Logic behind shuffled order of pages

(Hidden) symmetries examples in probability

Which dates have Month-Day-Year and Day-Month-Year representations that are perfect squares? (eg, Sept 27, 2025: $9272025=3045^2$, $27092025=5205^2$)

How can I count the number of possible assemblies of a 32-piece puzzle given an adjacency list?

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