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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1
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1answer
65 views

Did the U.S. Army use a formula to evaluate fitness performance?

While writing a web app to calculate one's score on the Army Physical Fitness Test (APFT), I grew tired of simply retyping this chart: ...
1
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2answers
59 views

What is the fair price of the game below?

You are playing a fair die game with 'n' die rolls. You have decided on the "fair" price of the game. So, to take part in this game you need to pay upfront this value. Then you get to roll a die, n ...
4
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1answer
68 views

Difference Puzzles

I have a puzzle calendar that features 20 or so different types of puzzles. Some are pop culture references and some are logical. Anyway I can do most of the logical ones without breaking a sweat in ...
1
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3answers
82 views

Confusion about triangle formation.

A stick of unit length is cut in three parts. Whats the probability that it'll form a triangle. The condition which i used $x_2+x_2\geq x_3$ where they denote sides but i get probability as $\infty$ ...
0
votes
1answer
34 views

What is the likelihood of being killed by lightning in this situation?

There was a recent thunder storm in my city and it caused me to start thinking about a certain problem (perhaps it's my own, perhaps others have thought about it or some variant previously, I do not ...
5
votes
1answer
33 views

Manipulation with strings riddle.

Starting with the "string" $PI$, can I or not transform it into the "string" $PK$ by applying the following rules (each rule can be used any number of times, in any order, and $x$ and $y$ represents a ...
1
vote
1answer
50 views

Puzzle: What is the algorithm for finding the kangaroo

There is a kangaroo that placed somewhere on $L$ upon the axis of the natural numbers. At some point of the time, The bell is ringing and the game starts: Each round the kangaroo jumps $K$ steps ...
5
votes
3answers
132 views

Dwarfs over a bridge

300 dwarfs go over a bridge in the middle of the night. The bridge is rickety and manages at most two dwarfs at a time. With them is a lantern that they must provide at each transition. Dwarfs need ...
3
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0answers
78 views

Tablecloth & table problem

Friday night we threw an house warming party and invited quite a number of fellow students. To fit everybody around the table we had to enlarge it, pulling out two sort of shelves from the short ...
0
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2answers
100 views

Find the number to replace the question mark in between two pairs of numbers

Here is the problem: I have to find the number to replace the question mark. I know there is a series or a pattern to find it any hint will be very helpful.
1
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1answer
46 views

Probability Of Two Boys Puzzle (Standard vs Tuesday Boy)

For those that aren't familiar with Gary Foshee's probability puzzle/paradox from 4-5 years ago, you can find an analysis here: http://news.bbc.co.uk/2/hi/programmes/more_or_less/8735812.stm While ...
4
votes
1answer
108 views

What is the minimum number of squares to be drawn on a paper in order to obtain an 8x8 table divided into 64 unit squares? [closed]

What is the minimum number of squares to be drawn on a paper in order to obtain an $8\times8$ table divided into $64$ unit squares. Notes: -The squares to be drawn can be of any size. -There ...
2
votes
1answer
64 views

Puzzle about sorting coins while blindfolded

You have $n$ coins in front of you, and you are blindfolded. You know that exactly $10$ of the coins are showing heads, the rest are showing tails. How can you sort all the coins into two piles such ...
5
votes
1answer
91 views

How many $9\times 9$ squares can I cut from this figure (it's $38\times 40$ without some corners)

Can I cut 16 ones (along the grid)? I've tried to paint some $15$ cells so that every $9\times 9$ square contain only $1$ painted cell (so I prove there can't be $16$), but to no avail. The figure ...
2
votes
1answer
55 views

About a “99 similar and 1 not similar” problem

A great friend of mine recently sat for an interview. He was asked a question which has fascinated me since some days now. It is Consider you have 100 balls which look the same but one out of ...
1
vote
2answers
128 views

I want to write a Christmas message only with particular zeta values. It is possible?

I want to write a Christmas message to leave as a comment thanking the people who in the next 24th December will solve some of my problems: I wish you Math Christmas and a Happy New Year ... ...
4
votes
2answers
171 views

Seeing a pattern (puzzle) [closed]

Does someone see a pattern?: 1 11 21 1211 111221 312211 13112221 1113213211 31131211131221 13211311123113112211 111312211331121321113212221
1
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2answers
90 views

A number with 6 distinct digits which get multiplied by 5 if we move the last digit to front [closed]

There is a number with 6 different digits, if we pick the last digit of that number and place before that number we got $5$ times our number. How to find such a number?
2
votes
1answer
77 views

Pick a number that is better than your friends

Consider the following game. There are $n$ players, each one has to pick a (real) number $x$ between $0$ and $100$. There is one round to the game. The winner is the person whose number is closest ...
0
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0answers
36 views

Puzzle question (trick)

Is there a way to proof that this always works: Pick 21 different cards; Choose one card, and remember it; Place the cards on three accumulations (every accumulation is 7 cards); Choose the one with ...
0
votes
1answer
57 views

2-player game, putting coins on a round table [duplicate]

Two players place coins of identical size (say quarters) on a round table. Each player has to place exactly one coin on the table without overlap with the coins already on the table. The first player ...
1
vote
2answers
161 views

Eric has got 1 sum wrong

Eric has got 3 sum wrong each time he exactly pressed one wrong key \begin{align} 5+3+2 & =317 \\ 25+36 &=900 \\ 8+8+2 &=3 \\ \end{align} can you work out which key he actually pressed
0
votes
1answer
74 views

Is it worth playing this game of dice?

We pay $\$42$ so we can throw $3$ fair $6$ sided dice. We get back the product of the resulting dice values. Is it worth playing this game? What is the expected value of your winnings (or losings) ...
1
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0answers
30 views

Concrete solution to the (oriented) Oberwolfach problem with one table

The oriented Oberwolfach problem (with only one table) and its solution are the following. In a meeting of $n$ people during $n-1$ days (combinatorists at Oberwolfach for concreteness), they all have ...
0
votes
1answer
37 views

How to obtain fair competition between two teams

Consider a class with $4$ students having min goals as $\big\{ 1, 3, 4, 5 \big\} $ and max goals as $\big\{ 2, 5, 8, 6 \big\}$. Find the best way to divide the class in such a way that the match is ...
1
vote
1answer
35 views

Logic puzzle, numbers on the back of head

Ok, I found this puzzle and I can't figure out the answer: Two people, Albert and Bernard have a natural number {0,1,2,3 ...} on the back of their heads. Rules: They can't see their own number ...
2
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0answers
87 views

When solving a big Rubik cube (100x100x100), do you reduce the solution to like 50x50x50, and then 25x25x25, and then like 10x10x10 and then 3x3x3?

My question is about Rubiks cube. Say you're solving a 100x100x100 cube (you can see examples in youtube by computer program - https://www.youtube.com/watch?v=0cedyW6JdsQ) When solving a big Rubik ...
3
votes
2answers
51 views

Find an example of a non trivial Think of a number game

Everyone knows the game where someone ask you to think of a positive integer, then ask you to do some elementary mental operations and finally predict the result. Example: think of a number $n$, ...
1
vote
3answers
184 views

Bucket Puzzle Probability Problem

You have 2 buckets. One full of white marbles and the other full of black marbles (equal amounts). How do you allocate the marbles into two buckets in a way that maximizes your probability of picking ...
1
vote
1answer
88 views

Guessing larger of two numbers given finite range

A small twist on the classic probability puzzle: You are given two boxes with a number inside each box, each of which ranges from [A, B]. The two numbers are different but you have no idea what ...
4
votes
0answers
203 views

Geometry puzzle - Show that $x = y$ [closed]

Problem In the following figure, show that $x = y$. My attempts Sadly nothing of value. I have far too little experience with geometry to even begin trying to solve this.
2
votes
1answer
239 views

Find distance between two figures

I was trying on this problem. All information is in picture. The aim is to find $AB$. It looks very simple problem. I spent more than one hour to solve it but I can't. It looks simple,but equation ...
0
votes
0answers
25 views

How many digits of an $n$ digit positive integer do I need to know to correctly guess the first $m$ digits of the $k$ th root of $n$.

Please help me solve this puzzle, which in my opinion only sounds tough: How many digits (counting from the left) of an $n$ digit positive integer do I need to know to correctly guess the first $m$ ...
2
votes
3answers
64 views

How can one solve the tower of hanoi problem if there are discs of similar width in it?

For example a line with '1111' represents a disc with diameter of length 4. Similarly a line with '111' represents a disc with diameter of length 3. Below is the representation of a tower that has 5 ...
1
vote
1answer
31 views

Is every nonogram an erased version of a slightly fuller nonogram?

Say we have an $N\times M$ binary nonogram, where the $i^{th}$ row has to sum to $n_i$, and the $i^{th}$ column has to sum to $m_i,$ so that we have constraints $(n_1,\dots,n_N)$ for rows and ...
3
votes
3answers
132 views

Does there exist $n$ such that all numbers $n,2n,\dots,2000n$ have the same digits?

Does there exist a number $n$ such that all numbers $n, 2n, 3n, 4n, \dots, 2000n$ have the same multi-sets of digits except zeroes? (Having the same multi-sets of digits excepts zeroes means ...
-3
votes
1answer
60 views

birds and cages

We have a number of birds and we bought cages to put them in. If we put $7$ birds in each cage then one bird is left over. If we put $9$ birds in each cage then one cage is left over. Find the number ...
1
vote
3answers
84 views

Two riders and their distance

Two riders have distance between them $118$ km and they are moving towards each other to meet . B starts an hour later by A. A travels $7$km in hour while B travels $16$km every three hours. How ...
0
votes
2answers
36 views

Find the Number $N$

There is a number $N$ that if we add to him the number $100$ we take a square and if we add to him the number $168$ we take a square.Find this $N$ Any ideas would be apreciated for this puzzle
1
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0answers
45 views

1000 apples and 10 baskets

Someone asked me this question and I found the answer but I'm stuck proving it. We have 1000 apples and 10 baskets. Distribute apples in a way that if someone asks for any number of apples from 1 ...
0
votes
1answer
41 views

Parallel Coordinates Riddle: Is it possible to go from line to point to line .. and eventually come back to the same line?

For clarification: For a line that is represented in the Euclidean plane as: $l: a_1x_1 + a_2x_2 + a_3 = 0$ We can represent it using parallel coordinates by using the transformation $$ A ...
0
votes
0answers
48 views

Calculating horse racing odds by having some data.

I've seen a few similar questions but non of them give satisfactory answer. My question is connected with horse races. Assume we have a race with 6 horses and we are given following coefficients ...
0
votes
0answers
46 views

Is there a field size such that it makes perpetual “candy crush”

a.k.a Infinite Candy Crush Background: "Candy Crush Saga" is called a match3, but it has some "special" events that will eliminate all rows, eliminate all "candies" of a particular shape, or even ...
3
votes
2answers
101 views

N marbles puzzle: find the heaviest among them.

Suppose there are $N$ marbles and a two-pan balance used to compare the weight of 2 things. All of the marbles weigh the same except for one, which is heavier than all of the others. How would you ...
-2
votes
3answers
58 views

$3$ sons that must sell in the same price

A father send his $3$ sons to sell watermelons.The first son took $10$ watermelons,the second $20$ and the third $30$ watermelons.The father gave order to sell all in the same price and collect ...
-1
votes
1answer
55 views

Puzzle with twins

Dying someone appointed in the will the following: If his pregnant wife giving birth to a son , then she will inherit 1/3 of the estate and his son 2/3 . If giving birth to daughter , then she would ...
0
votes
2answers
46 views

Nine same balls with one heavier

There are nine same balls,which all weigh the same except one , which is heavier than each others from the rest. How we can with just two weighings to find out which is the heavier ball?(We are using ...
0
votes
3answers
35 views

how many birds would buy from every species?

A farmer sells chickens,geese and ducks.Every chicken costs $100$ dollars,every goose costs $200$ dollars and every duck costs $250$ dollars.A customer wants to buy $40$ of these birds and spending ...
-3
votes
1answer
49 views

A student had to solve $26$ problems.how many problems successfully solved and how many wrong? [closed]

A student had to solve $26$ problems.His father promised that he will give him $800$ euro for every problem that we would solve correctly,but he would abstract $500$ euro for every problem that would ...
0
votes
1answer
43 views

Memory registers puzzle

There are 3 memory registers: A, B and C. Following are the 3 valid commands: 1) copy from A to C 2) copy from B to C 3) Replace A by A - C How can these commands be used to copy from B to A?