This tag is meant for questions about the mathematical principles behind games, riddles, or their possible solutions. If the answer is known to you please do not use this tag to "riddle" other users, but rather to ask about the correctness of a possible solution or ways to extend and improve an ...

learn more… | top users | synonyms (1)

12
votes
0answers
201 views

The Right Triangle Game

I am looking for a deeper understanding, particularly the optimum strategy and the maximum score as a function of grid size, of the following (single-player) game played with an $n$ by $m$ grid: ($6 ...
6
votes
0answers
118 views

Card passing game, maximum length

Quoting from this question: There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two ...
5
votes
0answers
102 views

How many points you should draw in the square at least?

There is a square, which side length is $2$, To ensure there exists a triangle in the square, with an area less than $0.5$, how many points should you draw in the square at least. the goal is for all ...
4
votes
0answers
99 views

How far away is that cloud?

A few weeks ago I was on an airplane and to pass the time started thinking about this problem. Using the following information, I wanted to know how far away a cloud I could see was. Under some ...
4
votes
0answers
87 views

Adding Numbers Pattern

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
4
votes
0answers
49 views

Would you please take a look if my substantiation is correct?

The four numbers 4, 5, 6, 7 are randomly inserted into 7 .3 .4 . 6 . 48 The result is a ten-digit number - for example, 7 4 3 5 4 6 6 7 48 How high is the chance, that the number created is ...
4
votes
0answers
154 views

Puzzle - zero knowledge proof

I am solving the following problem : I have edge-matching puzzles, where all pieces are squares and the grid has $n$*$n$ format. There is no global image to guide a puzzle solver. Despite the puzzles ...
4
votes
0answers
88 views

Find the number that follows the rules of two different series

I have this logic problem where I need to find a number that fits in 2 different series (vertical and horizontal). Each series has a rule, and once you find them, you can determine the answer. $$ ...
4
votes
0answers
131 views

Whats the mathematics behind this type of taking the rope out puzzle.

I know there has to be a way to solve this puzzle with math. I have included a picture, because I don't know the proper terms for this puzzle. I have included two pictures, I believe they are the ...
4
votes
0answers
312 views

A product puzzle

This is from a math contest. I have solved it, but I'm posting it on here because I think that it would be a good challange problem for precalculus courses. Also, it's kind of fun. Write the ...
3
votes
0answers
68 views

A game on a smaller graph

In this question Alice and Bob play a game on $K_{2014}$, Alice directing one edge, Bob directing $1$ to $1000$ edges with Alice trying to make a cycle. The proof that Alice can win depended on the ...
3
votes
0answers
107 views

History of a combinatoric problem: exchanging numbers by throwing stones

Another user recently asked a question on the Puzzling stack: Two spies throwing stones into a river. Suitably generalised, it becomes: Two spies (Alice and Bob) need to exchange a message. Each ...
3
votes
0answers
98 views

Fisherman riddle: Combining probabilities

This is more a probabilities problem than a riddle. The riddle is: I am in a village, where a fisherman lives. The fisherman tells me that there is a 70% possibility that it will rain tomorrow. I ...
3
votes
0answers
166 views

Limits of infinite processes that terminate in finite time - checking my understanding?

I am a computer scientist by training, but have a fair amount of math background that I've picked up through classes, teaching, and general interest. A student of mine posed a question to me. I think ...
3
votes
0answers
118 views

The Fox And The Duck Puzzle

A duck, pursued by a fox, escapes to the center of a perfectly circular pond. The fox cannot swim, and the duck cannot take flight from the water. The fox is four times faster than the duck. Assuming ...
3
votes
0answers
76 views

Another machine problem

This is linked to my previous question Discounted optimization problem I have difficulties again finding a formula for $F(x)$. We consider a machine at time $t$ which is in state $x$. The machine ...
3
votes
0answers
62 views

Calculating that confidence that pairs of lightbulbs are independently illuminated.

So, you're sitting in a dark room, and on the far wall you see $n$ lightbulbs mounted above plaques numbered $1$ through $n$. There is a lightswitch on the arm of your chair. Every time you flip the ...
3
votes
0answers
143 views

Can this be only solved by trial and error?

The following question was asked in a competitive exam Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the ...
3
votes
0answers
76 views

Question, need help finding the source.

I was hoping someone could tell me if they knew the source to this problem: Let S be a subset of {1, 2, 3, 4,..., 10, 11}. We say that S is LUCKY if no two elements of S differ by 4 or 7. The ...
3
votes
0answers
100 views

Least characters in a numerical representation of integers

I was wondering what the shortest way to represent any given number is. For example, $387420489=9^9$. So, for this case, the smallest representation is of order 2 (2 numbers). Alternatively, ...
2
votes
0answers
30 views

Cookie Clicker Chocolate Egg strategy

Introduction Cookie Clicker is a silly Javascript based web game. Here is a brief description of what you do: (description taken from this question: Explain a surprisingly simple optimization result) ...
2
votes
0answers
69 views

permutation and combination advanced

I have n sets having values less than 100. I need to find how many arrangements could be made if I pick one element from each set such that in the given arrangement there are no duplicates? NOTE: A ...
2
votes
0answers
42 views

Number of tries to guess M-1 letters from M-letters-code.

There are N letters in an alphabet. There is a combination lock, the code to it consists from M different letters. You can input M letters combination to try to open the lock. If you guess at least ...
2
votes
0answers
73 views

A mathematical game: moving tiles

There is a mathematical game called moving tiles. There are $8$ different movable tiles on a $3 \times 3$ board, At the beginning the tiles' location is given as following: ...
2
votes
0answers
278 views

What is the highest possible score in 2048 hard?

There is a variant of the popular game 2048, called 2048 hard or 2048 impossible, which automatically places each new tile in the hardest possible location. Is this variation possible to solve, and if ...
2
votes
0answers
82 views

Given a number of items, how many sets of three are there where no two sets are two thirds similar?

Sorry if the title isn't proper math-talk. Hopefully I can explain it better here. So let's say we have a set. 1, 2, 3, 4, 5, 6, 7, 8, 9. I want to know how many groups of three can be made where no ...
2
votes
0answers
71 views

Maximizing an algebraic expression using brackets

It's a riddle of sorts: given a list of numbers $\alpha_1 \dots \alpha_n$ and operators $o_1 \dots o_{n-1}$ which can be only $\times\, \mbox{or}\, + $ if the above is a specific algebraic expression ...
2
votes
0answers
85 views

placing coins on a table with a twist.

consider the classical puzzle, on a circular table, you and a friend take turns placing coins on the table and the first person who cannot do this loses. You can guarantee winning by placing the ...
2
votes
0answers
62 views

Minimum Overlap

You have a set of ten numbers, and you are trying to cover all 4-element subsets of this set. To do this, you choose 5 elements from the set every time and you cover all 4-element subsets of your ...
2
votes
0answers
144 views

Make one cube out of 8 little cubes

As part of a puzzle, you have to stack 8 little $1\times 1\times 1$-cubes so that they form one big $2\times 2\times 2$-cube. Now I want to check all possible solution to the puzzle and therefor I'm ...
2
votes
0answers
107 views

Can 24 lines on a cubic surface be realized as 24 identical spiral rods?

It's possible to put 24 lines on a cubic surface. 27 lines is possible, but I don't have a great picture for that surface. It turns out that the 24 lines can be built with Zome. I'm thinking that ...
2
votes
0answers
81 views

Is there a use for this technique?

I remember reading once about the following algorithm: Consider a lattice grid and $N$ houses situated at grid points, in which live the town elders. They want to choose a lattice point location ...
2
votes
0answers
522 views

Four candle problem: Using candles as timers

The candles each take one hour to burn completely. Cutting off bits of the candles is forbidden, but the candles are placed on a raft of fork handles so they may be burnt at both ends (e.g. to time ...
1
vote
0answers
39 views

A good book with algorithmic puzzles with solutions (not of kind “how to pass and IT interview”)

can you please advise me a book with algorithmic and mathematical (IT-oriented) puzzles. But I want not one more book of kind "How to pass an interview in Microsoft / Google / any other big company" ...
1
vote
0answers
36 views

Number of solutions to sudoku puzzle

Inspired by this question, consider hints on a Sudoku board. A regular puzzle has a unique solution. It is clear that there are puzzles with 2 or 3 solutions, and therefore, I guess, puzzles with say ...
1
vote
0answers
49 views

R. Jeffrey and the Three Prisoners

Here’s something curious, from p. 26 of the estimable Richard Jeffrey’s last, posthumously-published book, Subjective Probability: The correct (or at least orthodox) answer to this puzzle would be ...
1
vote
0answers
58 views

Snake cube puzzle equation

This is a Snake Cube Puzzle I am trying to understand the solution from mathematical point of view. Someone even wrote a solver: https://github.com/markfickett/snakepuzzle but I can't really read ...
1
vote
0answers
70 views

Hanging a picture with Beta functions

There's a classic puzzle that goes something like this: You have two nails in a wall, and you want to hang a picture with a string (think of a necklace with a pendant) in such a way that if you ...
1
vote
0answers
73 views

Number of paths in a grid

A common puzzle problem is to count the number of paths that start from the bottom-left-hand corner of a grid and end at the top-right hand corner, with the restriction that you can only move upwards ...
1
vote
0answers
58 views

Math Puzzle, finding a sequence with a certain property

A certain number of the $5000$ members of the Conway Mathematical Society (each of which has a different membership number between $1$ and $5000$) got together to discuss a puzzle. Much to their ...
1
vote
0answers
93 views

Riddle about dog running in company of soliders

A group of soldiers march together straight in square formation $50 \times 50$ meters. There is the dog at the back of the formation. Dog starts to run towards the first line of soldiers and then when ...
1
vote
0answers
114 views

Wedding Vows puzzle

My father came up with a puzzle and dared me to solve it. I could solve it by trial and error, but I rather want to solve it mathematically. It is the so called "Wedding Vows puzzle" where you have to ...
1
vote
0answers
53 views

When does a ball in a game of brick breaker never hit the remaining breaks?

I have a block size 2N*2N and some squares are filled with bricks and some aren't. I have a ball that travels distance 1 in the x and y direction and bounces off with perpendicular direction if it ...
1
vote
0answers
51 views

Finding the maximum number of voters satisfied in a ballot

Suppose you are given a file with the following information: 3W 4M 5 M2 W1 M3 W1 W2 M4 M1 W1 M4 W3 The top line specifies the number of candidates in each of two ...
1
vote
0answers
47 views

Visually apealing holologous transformation of a given contour

There is this problem which roughly says: You want to put a framed picture onto the wall with a cord to the picture frame. The cord is a single one, and both ends are attached to the frame. ...
1
vote
0answers
543 views

what is maximum number of points of intersection between the diagonals of a convex octgon?

What is the maximum number of points of intersection between the diagonals of a convex octagon (8-vertex planar polygon)? Note that a polygon is said to be convex if the line segment joining any two ...
1
vote
0answers
387 views

Cryptography puzzle

I'm currently broadening my knowledge in cryptography (or, at least, am trying to) and so I stumbled upon a puzzle I can't crack. It goes like this: You're given a set of pairs. The second number is ...
1
vote
0answers
74 views

What is the optimal investing solution for the given simulated market?

I have come across an artificial, simulated, stock-market type of situation, whose rules, I find, create a rather interesting problem. I want to know if there is a mathematically optimal solution for ...
0
votes
0answers
21 views

Ternary balance with unknown weight

Main references: Ternary (Wolfram MathWorld) Balanced ternary (Wikipedia) Weighing scale: Balance (Wikipedia) <quote> Balanced ternary has other applications besides computing. For example, a ...