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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0answers
31 views

Dice game puzzle [duplicate]

Playing a dice game against an opponent. Three fair 6 sided dice are used. But they are special- each dice has three distinct numbers b/wn 1 and 9, with pairs of opposite faces printed on identical ...
21
votes
2answers
330 views

The Plank Problem 2 Dimensions

We were trying to solve this wonderful problem, but have not succeeded to solve. It goes like this: Let $R=[0,1]^2$, and $D\subseteq R$ be a convex set which intersects each side of $R$. Define a ...
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5answers
126 views

game theoretic die rolls

Suppose player X has a 6 sided die and player Y has a 10 sided die. They each get two rolls and they can each choose to stop rolling on either one of the rolls, taking the number on that roll. Whoever ...
6
votes
1answer
95 views

Riddle: Best caller

Assume we have an closed interval $I = [a,b]$ where $a,b\in\mathbb{R}_+$ ($a,b\geq0$). Three persons pick a number each in the interval, lets call the numbers $A$, $B$ and $C$. We then look at 1/3rd ...
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3answers
56 views

Permutation and Combination Puzzle - Spy Keypad

Keypad 1 2 3 4 5 6 7 8 9 J. Bond has to break into the headquarters of an evil organization and steal important documents. The documents are in a safe that can ...
2
votes
0answers
275 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 ...
1
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1answer
49 views

Piping three circles to three squares

How I can prove the impossibility of joining three circles to three squares with non-intersecting lines (not strictly straight). Shapes of squares and circles are only representative. Each circle ...
4
votes
2answers
104 views

expected value of a game with a n sided die

Suppose we have a n-sided die. When we roll it, we can be paid the outcome or we can choose to re-roll by paying $1/n$. What is the best strategy and what is the expected value of this game? As an ...
5
votes
1answer
132 views

Rooks in 3D chess board

How many rooks are needed for a 3D chess board of size NxNxN so that every empty cube on the board can be reached by a rook in a single move?
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votes
1answer
30 views

Puzzle about total winnings in a card game

Mr. White is playing with Mr. Green. They decided that stake of every round will be 50% of total money that Mr. Green has. Mr. Green said that he has in total 32$. So in the first round stake was ...
0
votes
2answers
61 views

Puzzle about probability of colour of a billiard ball left in a bag

A bag contains one billiard ball. It can be white or black (with equal probability). We put a white ball inside the bag (so now there are 2 balls in the bag). Now we take one ball from the bag. It ...
1
vote
2answers
84 views

hitting a dart board probability

You have a dart board which is split in half. If you hit the left half, you get $2$ points, if you hit the right half, you get $3$ points. You have an 80% chance of hitting the dart board on any ...
3
votes
1answer
77 views

Pure algebra…

There are 5 balls with different unknown weights. We know that the weights of all possible pairs are 16,18,19,20,21,22,23,24,26,27. What are the weights of the ball? Just to verify, is the sum of ...
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votes
0answers
28 views

Random permutation with a scientific calculator

I have 8 people whom I want to divide into 2 groups. The allocation must be uniformly at random, i.e., every person must have equal probability of joining either group. We came across a situation ...
1
vote
1answer
59 views

52-card trick for a larger deck?

Long ago someone demonstrated the following card trick with a standard 52-card deck: (1) A volunteer selects 5 cards from a shuffled deck, which the performer does not see. (2) The assistant puts ...
0
votes
1answer
31 views

Convex Hexagon with one-sized angles property

Let P be a Convex hexagon that all is angles are on the same size. I want to show that every pair of opposing edges has the same difference (if one edge is in the size $x$ and it's opossing edge is of ...
0
votes
2answers
78 views

What comes next in the series?

Well, here is a numerical sequence puzzle, which I really tried hard, but still could not find the pattern? 2 4 6 30 32 34 36 40 42 44 46 50 52 54 56 60 62 64 66 x? Can anybody help me out in ...
12
votes
4answers
612 views

expected value of a sum of a 10 sided die

Suppose you have a fair die with 10 sides with numbers from 1 to 10. You roll the die and take the sum until the sum is greater than 100. What is the expected value of this sum?
-1
votes
1answer
63 views

The Bixby boys puzzle [closed]

It was the first day of class and Mrs Feldman had two identical looking pupils, Donald and Ronald Bixby, sitting next to each other in first row. "You two are twins?", she asked. "No", they ...
3
votes
3answers
68 views

Weighing puzzle

6 balls, 2 with New York logo. 2 with California logo, and lastly 2 with Texas logo. In each pair, one ball heavier than the other. The heavier ones weigh the same, so do the lighter ones. You are ...
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
votes
2answers
98 views

Math brain buster [closed]

Amon, Beta, and Cora each have 2 occupations from the following list: dentist, engineer, teacher, painter, writer, lawyer. No two have the same occupation. a. The dentist had lunch with the ...
1
vote
4answers
126 views

Number puzzle, number arrangement

Arrange all of the digits from the numbers 1 through 15 in such a order that the sum of any adjacent pair is a perfect square. No repeats. I can be staring at those number for days. But I wonder if ...
1
vote
1answer
39 views

counting of numbers

In a garden there are three kind of roses-red, yellow and white. No matter which 9 roses are selected at least 2 of them are white; and no matter which 10 roses are selected at least 2 of them are ...
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votes
4answers
62 views

Puzzle: Minimum total distance to few points on the same straight line

You have 9 friends living on a straight street in houses: A,B,C,..,H,I The distance from the beginnig of the street(from the left) for each house is: A– 1.1 ...
2
votes
2answers
112 views

Making a biased coin flip fair

I have a puzzle: Two groups want to break a tied vote using a simple coin flip, however the only coin they have available is a biased coin (i.e., one side will come up more often than the ...
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 ...
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votes
1answer
47 views

Puzzle about spider in a shed of prism shape and shortest distance from one vertex to another.

Spider likes to walk in a shed during the night. It can walk on its floor, walls, ceiling. The shed is a prism. Dimension of shed is a x b x c. What is the closest ...
5
votes
3answers
456 views

Puzzle about six travellers going through bridge above canyon with an oil lamp

There is a dark night and there is a very old bridge above a canyon. The bridge is very weak and only 2 men can stand on it at the same time. Also they need an oil lamp to see holes in the bridge to ...
0
votes
2answers
69 views

Three friends problem.

Once there were 3 friends A, B, C. They went together to have a lunch at a hotel. The lunch they had costed 60 according to the menu. They paid the bill each one contributing 20. But when the waiter ...
0
votes
3answers
78 views

A mental question

We are given a rectangle whose perimeter and area are equal. We have to find their length and breadth.(Both length and breadth should differ). I solved the question via hit and trial method and got ...
1
vote
3answers
875 views

Answer to popular mathematical riddle

I recently run into a question that asked me to find a number $n$ if for $k$ times, $n$ has been halved and subtracted $0.5$ and, at the end, $n$ becomes $0$. I don't know if this is of any relevance ...
3
votes
2answers
305 views

Frog Jump Problem

Lotus leaves are arranged around a circle. A Frog starts jumping from one leaf in the manner described below. In the first jump it skips one leaf,next jump it skips two,three the next jump ...
1
vote
1answer
80 views

Number puzzle from NAPLAN practice quiz, I know the answer, but I can't figure out why it is the answer

Consider this puzzle: The answer given by the website is 10 (filled-in already in the picture) But I can't figure out why this is the case. My various thought processes so far have been: The ...
1
vote
2answers
376 views

How many distinct ways to climb stairs in 1 or 2 steps at a time?

I came across an interesting puzzle: You are climbing a stair case. It takes $n$ steps to reach to the top. Each time you can either climb $1$ or $2$ steps. In how many distinct ways can you ...
3
votes
1answer
106 views

Magic Squares with Lucas and Fibonacci Numbers

I am quite curious about can we construct magic squares using only Lucas and Fibonacci numbers(of course not repeating them? If yes, how can we construct them? And if not , what is the proof?
1
vote
2answers
41 views

Arrangement of Numbers to Get a Common Sum

I'm having trouble with a math problem. I need to arrange 6 numbers on a certain diagram: At every intersection of two circles, I have to put one of these six numbers: 4, 5, 5, 6, 6, or 7. The sum ...
3
votes
1answer
158 views

Apparent paradox for the bird traveling between two trains puzzle

Gretings. Trying the "hard solution" for the puzzle below (which has been discussed, with a different angle, elsewhere on this forum) I got to a point where I have three seemingly valid solutions, ...
3
votes
1answer
38 views

is diffrence of raduis of 2 circles is not depend upon thier peremeter

I read on the Internet it's true, but I suspect it: Image describing the puzzle Take a ribbon tightly wound around the equator of the earth. Add 1 meter to that ribbon by cutting it at any ...
4
votes
1answer
65 views

Is there a way to divide an integer-sided square into integer-sided non-right triangles?

Integer-sided right triangles will fit into a square: but how about integer-sided non-right triangles? Here's a near miss - they don't quite fit like this: Is it possible?
0
votes
1answer
68 views

Demystify / Solve a number progression.

I've worked on this for two days and haven't gotten anywhere. They don't seem to grow by an even percentage, nor by an incremented percentage, nor by a flat number increment. (as far as my limited ...
6
votes
2answers
169 views

Regularities when $n$ and $2n$ contain the same digits

Suppose we would like to find positive integers $n$ such that the base-10 representations of $n$ and $2n$ contain precisely the same digits. $142857$ is a well-known example, and computer search ...
10
votes
1answer
518 views

Interview Question Asked In yahoo

Can you find the smallest positive number such that if you shuffle the digits of the number in a particular order, the shuffled number becomes twice the original number. Source: ...
0
votes
1answer
93 views

Help in figuring an optimum spider speed [closed]

When a spider threw its web at a fly then one end of the spider's web sticks to the fly and the other one to the table's surface. The fly immediately tries to pull away from the spider's web and ...
0
votes
3answers
117 views

Probability that a leap year has 52 Sundays

For the Question "Find the probability that a leap year has 53 Sundays". The Solution goes : For 53 Sundays, we proceed as: $\frac{366}{7} = 52.28$; So we can be sure that there are 52 Sundays, ...
1
vote
3answers
64 views

Find Differences between Ages of A and B.

Question: A says to B, I am twice as old as you were, when I was as old as you are. If the sum of ages is 63 years. Find the difference between their ages. My Question: I understand that we need to ...
0
votes
1answer
61 views

Liar - Truth-Sayer - Tourist Problem. Construct the answer with the given 2 sub-statements.

A tourist A comes to a country where people are divided into two categories: Liars (L) and Truth Sayers (T). Ls always lie and Ts always speak the truth. Intending to walk to the capital, the tourist ...
28
votes
4answers
551 views

Fibonacci numbers from $998999$

Is there a nice explanation of ...
0
votes
1answer
74 views

The famous Portia's casket problem

Gold casket: the portrait isn't in the silver casket. Silver: the portrait isn't in this casket. Lead: the portrait is in this casket. At least one of the statements was true and at least one of them ...
2
votes
1answer
66 views

Generating functions and the blue eyed daughters

There is a famous problem, given that a man has a number of daughters and if you were to meet two of them at random there is a 50% chance that both have blue eyes. How many daughters does the man ...