# Tagged Questions

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 ...

232 views

### Problem regarding the fitting cube into sphere

I was solving the following problem Suppose I have a sphere of radius 1 metre. The sphere is colored with red and blue such that it has disconnected regions of red and blue colors. Now I have to ...
2k views

### Star of David Math Puzzle

My son brought the following puzzle home from his 3rd grade math class. Are there any strategies for solving it besides brute force?
431 views

### Minimum number of weighings necessary

8 boxes each having different weights are numbered from 1 to 8 (the lightest 1, the heaviest 8). The total weight of 4 boxes are equal to the other 4’s total, and your task is to identify these two ...
64 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. ...
178 views

### A riddle - is there a way to solve it non-numerically?

So the riddle is: John has written down $k$ sequential odd numbers: $n_1, n_2, ..., n_{k-1}, n_{k}$ (where $n_{2} = n_{1} + 2$ and so on). We know that: The sum of the first four numbers is a ...
405 views

### Fraction of the area of a square occupied by a circle

We have the following picture: The radius of the larger circle is twice that of the smaller circle. Find an expression for the fraction of the area of the square which is occupied by the two ...
1k views

### Math Puzzle - Fishing

One day 3 men (Ed, Eddie and Eric) decided to go fishing. They agreed that everyone takes one third of the total number N of fish caught. After fishing they went to sleep. At 3:00 AM Ed woke up. He ...
1k 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 ...
104 views

### A fly on a triangle?

A fly is on the vertex of a triangle. It can move left with probability $\frac 12$ and right with probability $\frac 12$. What is the expected number of moves till it reaches its starting point? ...
2k views

### How to create models for solving logic puzzle

this is not about getting an answer for this problem, but to create models for solve them, below I will show a simple puzzle in order to demonstrate what I mean: Lets say two friends just left a bar ...
113 views

### Right triangle with equal permeter and height - how to find side lengths?

The question: Suppose there is a right triangle with sides $a$ and $b$ and hypotenuse $c$. Its perimeter is the same as its area, and $b = 6$. What are its side lengths? I just cannot figure ...
184 views

### Where can I find Putnam competition questions and solutions online?

Math people: Until recently, at least, there existed at least one Web page containing complete Putnam competition problems and solutions from the past twenty years or so. In retrospect, I see that I ...
14k views

### Blue eyes: a logic puzzle

Today I read the Blue Eyes puzzle here. I also read the solution which I find quite interesting. But there are three follow up questions which I don't know the answer to: What is the quantified ...
233 views

### How to efficiently generate a sequence of random integers that adds up to 1?

I want to randomly generate a sequence of 10 integers in the range [-2, 2] that add up to 1. The distribution of the outcome isn't important. I just want the sequence to be random and the sum ...
104 views

### How to find the minimum expression(s) of a set of fixed-width bit fields?

If we define $x_1 x_2 \cdots x_n$ as a bit field of width $n$, and each element $x_i$ may be $0$, $1$, or wildcard $*$. A set of 4-width bit fields $\{0000, 0001, 0100, 0101\}$ can be aggregated ...
67 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 ...
1k views

### Riddles with a mathematical twist

I am looking for riddles that are understandable for everyone(so especially non-mathematicians) but require mathematical knowledge or deep abstract ideas to be solved. The best answer will be the ...
294 views

### Math Riddle Problems

My numerator AND denominator are both prime numbers less than 10. I am more than 1/2. I am less than 1. I am nit equivalent to 8/12 or 10/14. -What number am I? If you double me, I'm more than 1. If ...
2k views

### probability that broken sticks will not form a triangle.

A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio 4:3. What is the probability that the three ...
214 views

### Which set of preferences for three candidates is impossible?

Hi recently i appeared in an aptitude,there was a problem that i realy cant understand please provide some idea, how to solve it.( sorry to for poor English.) (Question)-> Three candidates, Amar, ...
2k views

### “The Original IQ Test” — A peg puzzle

Many of you may be familiar with a puzzle game that consists of a 15-peg triangle and is dubbed as "The Original IQ Test". The idea behind the game is that you fill 14 of the 15 holes with pegs, and ...
165 views

### Least amount of steps to get over 1000

I am wanting to type out 1000 characters onto a message, I start off with one character and I have that character in my clipboard. I then paste it to get two characters. From here I can either select ...
6k views

### Jigsaw Puzzle Help

I have a puzzle I'm trying to solve and I have all the border pieces set out but I'm pretty sure some are missing. How do I figure out how many pieces are in the border? It's a 1000 piece puzzle and ...
13k views

### Slice of pizza with no crust

The following question came up at a conference and a solution took a while to find. Puzzle. Find a way of cutting a pizza into finitely many congruent pieces such that at least one piece of pizza ...
849 views

### How to find the missing number

How to find the missing number $\{14,36,25,25\},\{20,50,20,10\},\{36,54,7,?\}$ answer was $3$ , but I dont understand why? well these four sets of numbers were kept in four seperate circular plate ...
301 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 ...
686 views

### how many returning ants will meet an ant which is going from $A\to B$?

A stream of ants go and return via same path from point $A\to B\to A$ with constant velocity, FROM ANY GIVEN POINT TWO ANTS PASS BY PER SECOND IN ONE WAY.It takes one minute to go $A\to B$ for any ...
598 views

### Solving the continuous mice problem

The classic Mice Problem considers 4 mice standing on the four vertices of a square, and at some point every mouse starts running after its clockwise neighbour in a clockwise manner. It is not too ...
203 views

### A puzzle on gcd

Consider a directed graph whose nodes are positive integers. There is a directed edge from $a$ to $b$ if $a<b$ and $a$ is relatively prime to $b$, i.e. $\mathrm{gcd}(a,b)=1$. Given two integers ...
154 views

### Are there connected, planar graphs of size $N$ with minimal degree $\left( N−2 \right)$ for any $N \in \mathbb{N}$?

I was doing a bit of doodling today with graphs of N vertices, trying my best to make sure that every vertex had minimal degree of $\left( N-2 \right)$ without any crossings. I was able to form ...
489 views

### Knight on a chessboard moving from a1 to h8

I was given a puzzle to solve which goes as:- Can a knight start at square a1 of a chessboard, and go to square h8, visiting each of the remaining squares once on the way ? I reasoned that this won't ...
614 views

### Explain a surprisingly simple optimization result

The following optimization problem came to my attention as an idealization of the silly browser game Cookie Clicker, but is representative of a range of strategy games: You have an initial ...
101 views

### Keeping a dynamic-dimensioned square centered in a rectangle

For some reason this problem which seemed fairly easy on the surface has given me a lot of trouble. I have a square who's side length changes based on an independent variable. The square's upper left ...
189 views

### Efficiently identifying spam honeypots

I realise that the title is computing specific, but I think the underlying problem is general - I just don't know how to phrase it more generally (which may be part of my problem). So I am asking ...
238 views

### Dice probability puzzle

What is the probability of a run of at least 3 sixes when a die is thrown 5 times? I think I have the answer but from what I have been told its not the correct answer. Would someone like to help?
551 views

### The smallest amount

Using a pool of problems, 20 tests will be formed. -Every test should have the same number of problems. -Any problem should be included in at most 10 tests. -For every 5 tests, there should be at ...
1k views

### Birds Problem-Brain Teaser- Amazon interview question

Three people consider as A,B,C went for sight seeing. A,B and C each individually saw a bird that no other saw.(Eg: If A saw a bird the same is not seen by B and C) Each pair saw a yellow bird that ...
2k views

### Egg problem-Brain Teaser-Amazon Interview Question

A lady from the chicken farm gathers the eggs and brings it to sell it in the market. She sells the eggs but few eggs are left over. The 2nd day the left over eggs was doubled. Yet she sells the ...
184 views

### Given a desired coloring scheme for a stick, how can I brush it with the fewest steps?

If I want to color a stick (regarded as a line segment in one-dimensional space) to a desired coloring scheme using brush, how can I make it with the fewest steps? Notice that, new color will just ...
107 views

### Combinatorics puzzle

I am having a problem dealing with following topic: lets say we have set of numbers n = [ 1 2 2 3 ] and we want be able to get all two-elementary combinations out ...
67 views

### Non-uniform scaling

I have 10 numbers $x_1, x_2, \dots, x_9, x_{10}$ which sum to a total of $1,000$. I want to scale these numbers so the total is equal to $10,000$, however I don't want them to scale exactly. I'm ...
81 views

### How to determine which encryption system is being used?

I came across this question in a local contest. I was not able to solve it at that time. Also, no solution was provided. I was wondering if someone can help me to understand how to tackle this kind ...
477 views

### A puzzle on game theory

Bob and Alice are playing a game. They will start with an integer $n$. Alice goes first, in each turn, a player can choose an integer between 1 and 13 and that number is to be subtracted from $n$. ...
151 views

### An interesting puzzle

Here is a puzzle challenge for you: Suppose $X,Y$ are independent and identically distributed Random Variables. Show that $$P\{|X-Y|\le2\}\le 3P\{|X-Y|\le 1\}$$
258 views

### A troublesome logic puzzle.

Here're two distinct integers $x,y$, both greater than $1$ but less than $100$. Student $A$ and $B$ know the values of $xy$ and $x+y$ respectively. Let's hear their conversation. $A$: I don't ...
6k views

### What would have been our number system if humans had more than 10 fingers? Try to solve this puzzle.

Try to solve this puzzle: The first expedition to Mars found only the ruins of a civilization. From the artifacts and pictures, the explorers deduced that the creatures who produced this ...
185 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 ...
1k views

### How to understand the analog clock problem?

I know the answer to this riddle: How often does the minute hand pass the hour hand on an analog clock? I know they pass 11 times every 12 hours, but I don't understand how to get to it, no ...