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
votes
3answers
119 views

Average of the smaller of three random numbers from $0$ to $1$

A friend of mine claims he saw the following question on a math puzzle site:- What is the average of the smaller of three random numbers from $0$ to $1$? And they've given these options:- $A) ...
4
votes
1answer
356 views

A 5x5 board has 25 cells.The numbers $\{1,2,3,4,5\}$ are written on every row,every column and the two main diagonals.

A 5x5 board has $25$ cells. The numbers $\{1,2,3,4,5\}$ are written on every row,every column and the two main diagonals without any repetition. If the sum of the numbers of the diagonal below the ...
23
votes
4answers
1k views

Number of vectors so that no two subset sums are equal

Consider all $10$-tuple vectors each element of which is either $1$ or $0$. It is very easy to select a set $v_1,\dots,v_{10}= S$ of $10$ such vectors so that no two distinct subsets of vectors $S_1 ...
0
votes
1answer
31k views

I don't see the pattern.. does anyone understand this..? [duplicate]

Note.. the numbers are actually in a 7 x 6 grid.. graphics did not show here.. ...
0
votes
2answers
356 views

How to deduce this puzzle

Every station on the railway system sells tickets to every other station. Some new stations were added. 46 sets of additional sets of tickets were required. How many new stations have been added? How ...
3
votes
2answers
185 views

Number-Theoretic Coin Puzzle

There are three piles of coins. You are allowed to move coins from one pile to another, but only if the number of coins in the destination pile is doubled. For example, if the first pile has 6 coins ...
0
votes
1answer
3k views

How many triangle can be drawn with those points? [duplicate]

There are 7 points on the circumference of a circle.How many acute triangle can be drawn with those points. please help me to solve this problem.
2
votes
1answer
94 views

Maximal number of kings on a chessboard, but this time two can be adjacent.

How many kings can be placed on an $8 \times 8$ chessboard such that every king can capture (is adjacent to) at most one other king? I can do 26, but can not prove that this is optimal.
3
votes
0answers
207 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 ...
0
votes
1answer
46 views

Finding affiliation of a number to a finite number of sets of incremental numbers

I have different sets of incremental numbers starting from zero like this: $S_1=\{0,1,2,3\}$ $S_2=\{4,5,6,7\}$ $S_3=\{8,9,10,11\}$ Each set has the same cardinality. I want to know, given a ...
2
votes
1answer
5k views

The Blind Man and Coins Puzzle

There is a table on which, a number of coins are placed. You also know that there are as many coins with Heads up, as many coins with Tails up. You are blind folded and there is no way to determine ...
5
votes
1answer
605 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 ...
1
vote
2answers
167 views

Ant on a square [duplicate]

There is a square of side $1 m$ and an ant has to cross diagonally. However, it chooses to walk along the boundary so the distance covered by it is $2m$ and not $\sqrt{2} m$. This it does in two ...
2
votes
1answer
396 views

Sangaku: Find the Radii of the Inner Circles

Sangaku (算額) are Japanese geometric puzzles written on wooden tablets over 150 years ago. There have been several previous puzzles, but I didn't see this one. Find the radii of the two inner ...
1
vote
2answers
878 views

Math Riddles #10 - Car Meter Riddle

Today my car meter reads as 72927 kms. I notes that this is a palindrome. How many minimum kms I need to travel so my car meter find another palindrome?
5
votes
7answers
2k views

3 trams are coming every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come?

3 trams are coming to the stop every 10, 15 and 15 minutes. On average, how long do I have to wait for any tram to come? It's a practical problem, not some kind of a riddle for which I have a ...
1
vote
1answer
2k views

The 100 Coins Puzzle

There are 10 sets of 10 coins. You know how much the coins should weigh. You know all the coins in one set of ten are exactly a hundredth of an ounce off, making the entire set of ten coins a tenth of ...
1
vote
1answer
89 views

Maximum score for the game

Here is a game: There is a list of distinct numbers. At any round, a player arbitrarily chooses two numbers $a, b$ from the list and generates a new number $c$ by subtracting the smaller number from ...
1
vote
1answer
260 views

100 prisoners and a light bulb

I'm curious if there is a solution,however ineffective, for the puzzle when the prisoners do not know whether initially the bulb is on or off. Second, has several bulbs modification of the problem ...
0
votes
2answers
132 views

How many zeroes (at the end) will 10! have when written in base 3?

I can get the answer for the question by calculating 10! and then converting it to base 3 but is there a more logical point of view to this question which will mostly generalise the solution for this ...
5
votes
1answer
266 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 ...
6
votes
2answers
336 views

Relatively prime property verification

I am reading a computer science puzzles book. And I get the following question - "You have a five quart jug, a three quart jug and unlimited supply of water. How would you come up with exactly four ...
3
votes
1answer
186 views

Looking for a pattern in a math riddle

Looking to find a pattern but no idea how: $12\mathop{\square}21 = 86$, $13\mathop{\square}31 = 192$, $14\mathop{\square}58 = 389$, $14\mathop{\square}94 = \ ?$
2
votes
1answer
639 views

How to reason about disentanglement “tavern” puzzles?

It took me an embarrassingly long time to remove the ring from this rigid structure: What math could I use to solve similar puzzles? Topology and knot theory seem helpful, but I don't think they ...
0
votes
2answers
143 views

I have a button…(story problem)

Tom has a job. He is a button pusher. He works for 8 hours per day. his job at work is simply to push a button. He has some freedoms and some limitations. When he arrives to work each day he has 5 ...
3
votes
2answers
94 views

The king's reversal in the classical chess problem?

I was talking to my math teacher about the classical problem where the king loses a chess match against a peasent and he is asked to give him $2^n$ grains for the $n$'th square (where the squares are ...
0
votes
1answer
409 views

Striking off a digit from each of the numbers written in seven rows, while preserving arithmetical operations

Problem Strike off any digit from each number in seven rows (need not be at same place) and combine the same operations with 3 digit numbers to get the same addition. After this strike off another ...
8
votes
3answers
243 views

Eating a cake from the inside.

Imagine that you are in the centre of a cube of cake with a known size. In order to move you must eat the surrounding cake but you can only move within the restraints of the six obvious directions ...
1
vote
2answers
1k views

How do I find the maximum number of knights on a chess board?

I came across this problem and after thinking a lot I could not get any idea how to calculate it. Please suggest to me the right way to calculate it. Given a position where a knight is placed on ...
1
vote
0answers
67 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
4answers
941 views

Minimum number of objects required to figure out the issue

There 1,000 buckets, one of them contains poison, the rest of them are filled with water. They all look the same. If a pig drinks that poison, it will die within 30 minutes. What is the minimum number ...
0
votes
1answer
87 views

what is the minimum number of hints must be provide in a Sudoku with only one solution in order to reach the answer?

what is the minimum number of hints must be provide in a Sudoku with only one solution in order to reach the answer? Also if you are interested, please provide a reference.
0
votes
3answers
262 views

red and green apples

We can eat 3 apples per hour. We must eat: 3 green apples once per 2 hours. 4 red apples once per 3 hours. We can't eat fractions of an apple. The apples are named, the 3 green (A, B, C) and the ...
6
votes
1answer
123 views

Return of the lost ant 3D

Starting in the center of a sphere of radius 1, draw a path with the shortest possible length that intersects every plane that is tangent to the sphere. This question appeared as a generalization of ...
1
vote
1answer
583 views

tangram cannot get a square with a little square hole in the center

From a tangram or seven-piece puzzle (first picture), we cannot get a square with a little hole in the center (the second cartoon), the hole is also a square Why?
0
votes
1answer
63 views

Maximum number of knights on a $2 \times n$ ($n\ge 2$) board

So, the puzzle is what is the maximum number of knights one can place on a $2 \times n$ ($n\ge 2$) board such that no two knights can attack each other. Apparently there is a formula for this ...
2
votes
1answer
177 views

Number of horse races to determine the top three out of 25 horses [duplicate]

This is a short mathematical puzzle from mindciphers.com which says : The London racetrack needs to submit its top three horses to the Kentucky Derby next month in order to compete for a prize. ...
10
votes
4answers
647 views

Kings on a chessboard

In how many different ways can six kings be placed on a $6\times 6$ chessboard so that no one attacks the others? If the problem was asked for a $3 \times 3$ board and $3$ kings, then the answer ...
3
votes
3answers
189 views

TicTacToe with considerations of symmetry

It is not difficult to determine the number of possible games of tic toe, but what about when rotationally symmetric positions are considered equal? Please do not simply give me the number, I would ...
2
votes
1answer
480 views

probability of a word in a string

What is the probability of a word n characters long appearing in a string of m characters, in an alphabet of x characters? A word here is simply a string of characters contained in another string of ...
7
votes
2answers
428 views

Real guessing puzzle

Allow me to propose a modification of a previously asked puzzle. I would like to replace 100 in that puzzle by $\omega$ and replace $99$ by "all but one". A version of the puzzle was also discussed on ...
5
votes
2answers
8k views

How many times are the hands of a clock at $90$ degrees.

How many times are the hands of a clock at right angle in a day? Initially i worked this out to be $2$ times every hour hence the answer came to $48$. But then in case of $3$ o'clock and $9$ ...
4
votes
1answer
66 views

Get from point A to point B efficiently.

This is a question I thought about while crossing the street. Suppose you're standing at the bottom-left corner of a rectangle. Your goal is moving to the the top-right corner, efficiently, ...
3
votes
1answer
998 views

Find a number leaving a particular remainder with 3 different numbers

I have the following question: Let $N$ be the greatest number that will divide $1305, 4665$ and $6905$, leaving the same remainder in each case. What is the sum of digits of $N$. My approach ...
4
votes
3answers
113 views

Find two numbers whose ratio is $1/2$ using each non zero digit.

So in this question i first figured out that the numerator must be greater than $5000$ so that there are $4$ digits on the numerator and $5$ digits on the denominator. And then after a few random ...
32
votes
5answers
1k views

Can this ant find its way back to the nest?

So the puzzle is like this: An ant is out from its nest searching for food. It travels in a straight line from its nest. After this ant gets 40 ft away from the nest, suddenly a rain starts to ...
12
votes
1answer
177 views

Coloring 5 Largest Numbers in Each Row and Column Yields at Least 25 Double-Colored Numbers

This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice solution and illustrates an often useful technique. If it is unsolved after a while, I will ...
4
votes
1answer
2k views

Can you make an equilateral triangle from 3identical trapezoids?

Is it possible to make an equilateral triangle from 3 identical trapezoids? If so, what angles would be needed in the trapezoids?
15
votes
2answers
448 views

A “What's my vector?” game

Alice chooses a binary vector $V$ of length $n$ which is unknown to Bob. In each round Bob can choose any number of indices $i$ and then Alice tells Bob how many of the $V_i$ are set to $1$. The ...
0
votes
1answer
41 views

When would the first collision occur on A Golden March

From A Golden March from the futility closet. Draw a circle whose circumference is the golden mean. Choose a point and label it 1, then move clockwise around the circle in steps of arc ...