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 ...

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2
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3answers
711 views

Converting recursive function to closed form

My professor gave us a puzzle problem that we discussed in class that I could elaborate on if requested. But I interpreted the puzzle and formed a recursive function to model it which is as follows: ...
2
votes
1answer
205 views

How do you convert this diagram into a linear system of equations/matrix form?

Question: Given is the following pipe system: the pressure in a stationary state is at every end and cross-point (with exception of $K_i, i ={1,...,4}$) equal to the average pressure of the ...
3
votes
1answer
420 views

Matrix and Binomial Coefficients

Considering the construction of a matrix as follows. The $n$th row in the matrix is filled with the coeffcients of $x^r$ in the expansion of $(1+x)^n$ from the columns $2n$ to $3n$ inclusive and ...
14
votes
3answers
689 views

Puzzle: digit $x$ appears $y$ times on this piece of paper…

There are ten questions on a piece of paper. Your task is to fill in each blank with a positive integer less than 10 such that there is no contradiction. You can reuse any digit. The question is as ...
2
votes
3answers
609 views

Given a line segment $AB$ and a point $P$ inside a circle, can one construct a chord through $P$ congruent to $AB$?

This is a little exercise found in Robin Hartshorne's Euclid: Geometry and Beyond: I believe I have found a solution, which only exists when $AB$ has length at least that of the chord bisected by ...
3
votes
2answers
253 views

13 integers with each set of 12 integers

Take 13 integers. Prove that if any 12 of them can be partitioned into two sets of six each with equal sums, then all the integers are the same. Does anyone know if the general case with 2n+1 ...
2
votes
4answers
550 views

Determine in How many ways $N!$ can be expressed as sum of consecutive numbers

Determine in How many ways $N!$ can be expressed as sum of consecutive numbers.For example for $3!$ can be as $1+2+3$ only $1$ ways. Please suggest an elegant approach.
3
votes
3answers
242 views

Maximize :: $A = B \times C$

Given $A = B \times C$ Using any $9$ digits form two numbers $B$ and $C$.All digits must be used exactly once. What is the maximum possible value of $A$?
6
votes
1answer
455 views

Guessing a hidden number on a cube

You are and your friend are given a list of N distinct integers and are told this: Six distinct integers from the list are selected at random and placed one at each side of a cube. The cube is placed ...
0
votes
1answer
84 views

4 machines producing 100mg, one of them is making 90mg, once chance to weigh 2 machines versus each other

You have 4 machines that are supposed to create 100mg chocolate bars. One of the four machines is not working correctly and is making 90mg chocolate bars. You only have 1 chance to weigh the chocolate ...
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 ...
1
vote
2answers
167 views

Construct a function to “increment” a value while asymptotically approaching a limit

Suppose I have a value $a_1$ such that $-L < a_1 < L$. I need to compute $a_2$ from $a_1$ and $b$, while satisfying the following requirements: $-L < a_2 < L$ if $b = 0$ then $a_2 = a_1$ ...
5
votes
1answer
777 views

How many possible combinations are there in Hua Rong Dao?

How many possible combinations are there in Hua Rong Dao? Hua Rong Dao is a Chinese sliding puzzle game, also called Daughter in a Box in Japan. You can see a picture here: ...
4
votes
6answers
2k views

Knights and knaves: Who are B and C? (task 26 from “What Is the Name of This Book?”)

I have the following issue #26 from What Is the Name of This Book? of R. Smullyan: There is a wide variety of puzzles about an island in which certain inhabitants called "knights" always ...
4
votes
1answer
423 views

Calculating Total Amount of Money Based on Weight

Dealing with US Dollars... Assuming we know the weights of half-dollars, quarters, dimes, nickels, and pennies. Also assuming the weights remain constant (don't change from one quarter to another ...
5
votes
1answer
2k views

Riddle (simple arithmetic problem/illusion)

I'm not sure how well known this "riddle" is but here it goes. 3 people go to a restaurant, each buy food worth 10.00. When they're done, they give 30.00 to the waitress. She gives the money to the ...
1
vote
3answers
372 views

Implication of three statements

Three fellows accused of stealing CDs make the following statements: (1) Ed: “Fred did it, and Ted is innocent.” (2) Fred: “If Ed is guilty, then so is Ted.” (3) Ted: “I’m innocent, but at least one ...
11
votes
3answers
605 views

Two seemingly unrelated puzzles have very similar solutions; what's the connection?

I think it's an interesting coincidence that the locker puzzle and this puzzle about duplicate array entries (see problem 6b) have such similar solutions. Spoiler alert! Don't read on if you want to ...
14
votes
3answers
931 views

Cutting a unit square into smaller squares

My algebra professor gave me this puzzle a while back. I'm pretty sure I've found the right solution; nonetheless, I wanted to share it and see if you come up with anything really nice or unexpected. ...
6
votes
4answers
2k views

3 Utilities | 3 Houses puzzle?

There's a puzzle where you have 3 houses and 3 utilities. You must draw lines so that each house is connected to all three utilities, but the lines cannot overlap. However, I'm fairly sure that the ...
3
votes
3answers
1k views

Using 4 '8's, get the number 24

Using only four 8's and only addition, subtraction, multiplication, and division.. how can you come up with the number 24? You may use fractions and decimals! But remember, you can ONLY USE four 8's
9
votes
1answer
449 views

Nice puzzle: 100 bread rings and two bags

You have two empty bags and 100 bread rings. The goal is to put all your rings into the bags in such a way that one of the bags will contain exactly twice as many rings then the other. ...
4
votes
2answers
249 views

Newspaper competition

A newspaper launches a competition. It said that readers should submit one number between 1 and 1000. A £2000 prize would be awarded to the person that got the closest to 2/3 of the mean of all the ...
9
votes
1answer
273 views

Ten people in a room

There are ten people in a room: Person 1 knows 9 people. Person 2 knows 8 people. etc. Person 9 knows 1 person. How many people does person 10 know? What is the answer and what is ...
4
votes
2answers
196 views

Particle moving at constant speed with Poisson setbacks

Consider a particle starting at the the origin and moving along the positive real line at a constant speed of 1. Suppose there is a counter which clicks at random time intervals following the ...
4
votes
2answers
346 views

Alien vs Alien Hunter Puzzle

I found this puzzle posted on a student website I frequent, but no one including the poster nor I could solve it. So I'm posting this puzzle here with hope that some of math whiz in here could ...
4
votes
6answers
641 views

A tedious puzzle (but not homework)

There are 1000 light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8...tutor 3 then 3,6,9...etc until all 1000 tutors have done ...
2
votes
5answers
4k views

The Three Nines [closed]

Possibly not a Math problem in the true sense of the word, but here goes. Three Nines - and various math operators = can be turned into various simple numbers. (9-9)*9 = 0 (9/9)^9 = 1 (9+9)/9 = ...
3
votes
1answer
243 views

There is a 5 by 5 matrix of points on a plane. How many triangles can be formed using points on this matrix?

There is a 5 by 5 matrix of points on a plane. How many triangles can be formed using points on this matrix?
11
votes
3answers
756 views

Covering ten dots on a table with ten equal-sized coins: explanation of proof

Note: This question has been posted on StackOverflow. I have moved it here because: I am curious about the answer The OP has not shown any interest in moving it himself In the Communications of ...
7
votes
1answer
340 views

License Plate Statistics

California issues license plates in numeric order (if we turn the letters into numbers). I have fun noticing the latest plate I have seen. I am interested in what you can derive from a series of ...
2
votes
1answer
206 views

When does an orthomorphism of the cyclic group exist?

I thought I would post (as a puzzle) one of my favourite results in combinatorics. I actually use variants of this result in research quite often. It's not impossible that someone will post an ...
4
votes
1answer
2k views

Party planning problem

Recently, I came across this problem in my textbook. Any hints on how to solve this using dynamic programming? "Professor Stewart is consulting for the president of a corporation that is planning a ...
11
votes
2answers
387 views

Packing disjoint family of discs with radii $\tfrac{1}{2}, \tfrac{1}{3}, \tfrac{1}{4},\ldots$ inside the unit disc

Does there exist a family of discs $\lbrace D_{n}\rbrace_{n=1}^{\infty}$ in the Euclidean plane such that the radius of $D_{n}$ is $\frac{1}{n+1}$, each $D_{n}$ is contained in the unit disc, and ...
10
votes
4answers
1k views

sangaku - a geometrical puzzle

Find the radius of the circles if the size of the larger square is 1x1. Enjoy! (read about the origin of sangaku)
4
votes
6answers
1k views

Finding the Heavy Coin by weighing twice

Suppose you have 100 coins. 96 of them are heavy and 4 of them are light. Nothing is known regarding the proportion of their weights. You want to find at least one genuine (heavy) coin. You are ...
17
votes
6answers
2k views

Tiling pentominoes into a 5x5x5 cube

I have this wooden puzzle composed of 25 y-shaped pentominoes, where the objective is to assemble them into a 5x5x5 cube. After spending quite a few hours unsuccessfully trying to solve the puzzle, I ...
6
votes
4answers
544 views

Mental card game

Each of n persons draws a card from a shuffled deck of $k$ cards numbered from $1$ to $k$. There are at least as many cards as persons. The winner is the person who is holding the largest card. If ...
4
votes
2answers
2k views

How to prove the optimal Towers of Hanoi strategy?

In the towers of Hanoi game, how do we know that we have the optimal algorithm for solving it? I thought about this and it seemed like any deviation from the standard strategies would be putting you ...
70
votes
5answers
3k views

Cutting sticks puzzle

This was asked on sci.math ages ago, and never got a satisfactory answer. Given a number of sticks of integral length $ \ge n$ whose lengths add to $n(n+1)/2$. Can these always be broken (by ...
9
votes
4answers
545 views

Irrational painting device

Part a) of the following problem appeared in one of the Putnam Exams (sorry, don't know which year exactly). If you want to solve Part a) don't read Part b). You have a painting device, which given ...
6
votes
2answers
328 views

Watchdog Problem

I just came up with this problem yesterday. Problem: Assume there is an important segment of straight line AB that needs to be watched at all time. A watchdog can ...
48
votes
5answers
8k views

Logic problem: Identifying poisoned wines out of a sample, minimizing test subjects with constraints

I just got out from my Math and Logic class with my friend. During the lecture, a well-known math/logic puzzle was presented: The King has $1000$ wines, $1$ of which is poisoned. He needs to ...
48
votes
21answers
3k views

Your favourite maths puzzles

Okay, so this question was bound to come up sooner or later- the hope was to ask it well before someone asked it badly... We all love a good puzzle To a certain extent, any piece of mathematics is a ...