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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-3
votes
0answers
32 views

Optimal solution and Answer [on hold]

Batman has devised a plan to lure Superman to a high rise building. His brilliant plan is to pour concrete over him to immobilize him, and then throw him off the building so that the concrete breaks ...
0
votes
0answers
30 views

Square of dominos with equal side sum

This is an assignment my sister in primary school got. I think they're supposed to solve it via trial and error, but I was wondering if there's a clever way to solve it. Lay the tiles of a double-six ...
2
votes
0answers
34 views

Logic problem: “John's safe's passcode'” question from earlier, with more detail [on hold]

The answer and explanations have already been given at its original post (on Facebook) but I'd like to confirm that it is indeed solvable since there are still some parts I don't quite understand. ...
0
votes
0answers
67 views

Is there a solution for this problem ?? [on hold]

There a man name john , john has a big safe but he forgot the password. he remembered : the password contain 10 distinct numbers If you add a certain digit in front, the aforementioned amount will ...
19
votes
2answers
2k views

Find a thousand natural numbers such that their sum equals their product

The question is to find a thousand natural numbers such that their sum equals their product. Here's my approach : I worked on this question for lesser cases : \begin{align*} &2 \times 2 = 2 + ...
2
votes
2answers
67 views

Next term in the pattern [closed]

$22+22=4444$ $43+46=618191$ $77+77=?$ What should come in place of $?$ I cannot see any logic in $43+46=618191$. Is there any?
1
vote
2answers
131 views

How many squares are in this image? Is there a method to check?

In this image I have counted 14 but others say 18. Is there a method to check exactly?
38
votes
4answers
5k views

Sharing a pepperoni pizza with your worst enemy

You are about to eat a pepperoni pizza, which is sliced into eight pieces. Each pepperoni will unambiguously belong to some slice (no pepperoni is "between" slices). The caveat is that you have to ...
1
vote
3answers
49 views

Logic with numbers

Nick wrote each of the numbers from 1 to 9 in the cells of the 3x3 table below. Only 4 of the numbers can be seen in the figure. Nick noticed that for the number 5, the sum of the numbers in the ...
1
vote
1answer
36 views

Maximise your profit in this die game!

You pick a nonzero number ($n$) of dice. The dice are tossed simultaneously until one, and only one, is a six. On success there is a payout of $p$ dollars. Otherwise, for each toss of the dice, there ...
0
votes
2answers
48 views

Minimum number of moves to even out a row of brick piles

Consider a row of $15$ piles of bricks. There is a total of 75 bricks, all identical. The number of bricks per pile varies across the piles. For instance, the distribution of bricks per pile might be ...
1
vote
2answers
60 views

A Problem Involving Two Sentries

Consider two sentries that are patroling on a road that is 2 miles long. They are sent to points chosen independently and at random on the road. I want to find the probability that the sentries will ...
0
votes
0answers
20 views

Another version of connecting ropes problem

Met this in an interview. Basically this is a different version of the old familiar rope connecting problem. In that problem, we are asked what's the expected number of loops after connecting n ropes ...
0
votes
2answers
27 views

Combine different denominations to form a sum

I am trying to do the Euler Project Problem 31 by hand. ( https://projecteuler.net/problem=31 ) Basically, I am asked how many ways I can form 200 pence by using the denominations 200, 100, 50, 20, ...
1
vote
2answers
51 views

What is the value of $xyz$?

Given an expression as : $$xyz+xyz+xyz=zzz$$ where $x,y,z$ are integers and $xyz$ represents a number for example $236$ (not to be confused with $x\times y\times z$), what is the number $xyz$?
9
votes
2answers
57 views

Sudoku grid guaranteed to be solvable?

I want to generate random sudoku grids. My approach is to fill the three 3x3 groups on a diagonal of the grid, each with the numbers 1-9 randomly shuffled. That looks e.g. like the grid below: ...
-2
votes
2answers
82 views

If $a,b,c$ are positive and integers, $a+\frac{1}{b+\frac{1}{c}}=\frac{25}{19}$, then $a+b+c=?$ [closed]

I've found this question and tried to solve it, but failed If a,b,c are positive and integers, $a+\frac{1}{b+\frac{1}{c}}=\frac{25}{19}$, then $a+b+c=?$ and how to get it?
0
votes
1answer
141 views

Maths Puzzle - Logic

Somebody asked me this puzzle, but they don't have answer to it. 1+2+3+4 = 61 2+3+4+5 = 52 3+4+5+6 = 51 4+5+6+7 = 50 7+8+9+10 = ? I want to know whether my reasoning and ...
1
vote
0answers
26 views

Proof to Theorem 3 in 'A modern treatment of the 15 puzzle' by Archer

I'm reading 'A modern treatment of the 15 puzzle' by Archer and cannot understand the proof to Theorem 3 and how they compute the permutation equation with their examples. My main problem is this ...
2
votes
2answers
42 views

Jeep problem variant: cross the desert with as much fuel as possible

I'm dealing with the following variant of the well-known Jeep problem: A 1000 mile wide desert needs to be crossed in a Jeep. The mileage is one mile / gallon and the Jeep can transport up to 1000 ...
2
votes
1answer
31 views

Variant of “prisoners and hats” puzzle with more than two colors

There are $n$ prisoners and $n$ hats. Each hat is colored with one of $k$ given colors. Each prisoner is assigned a random hat, but the number of each color hat is not known to the prisoners. The ...
1
vote
0answers
17 views

Oscillations in a Discrete Dynamical System.

If you are familiar with SingingBanana on youtube, he posted the following question: There is a 10 digit number where the first digit tells me how many 0 there are in the number, the second digit ...
0
votes
0answers
8 views

Transitive permutation groups & primitivity, 15-puzzle, Wilson

I'm reading the R. M. Wilson's paper about generalization of 15-puzzle to arbitrary graphs and I cannot understand the proof of following lemma: Lemma 3. Let $\Gamma$ be a transitive permutation ...
0
votes
1answer
92 views

Analogy between a Gödelian puzzle and Gödel's first incompleteness theorem

I'm studying Gödel's incompleteness theorems. And I have the following slide that defines a version of Gödel's first incompleteness theorem. The point is that one can always follow the math and get ...
-3
votes
1answer
460 views

Solve carefully [closed]

Solve carefully ... $$25-55+(85+65)=$$ You probably won't believe it, But this equals $5!$
2
votes
0answers
65 views

Number of ways to color a grid?

I have a $N \times M $ grid and I am trying to calculate the number of ways I can color this grid in maximum $k$ colors (I can use only $2$ colors or all $k$ colors) with the exception that two ...
0
votes
1answer
41 views

Choosing a number puzzle.

A and B play a game, where A begins the game. A can start the game by calling a number from 1 to 10, then the game continues by the other person choosing a number. But rule of game is if one picks x, ...
13
votes
4answers
1k views

What's the smallest number that we can multiply with a given one to get the result only zeros and ones?

I have the following set of numbers, $$4, 198, 4356, 10296, 14454, 25542, 31779, 51252, 53946, 99999$$ Let's take $3,4$ as an examples: The smallest number to multiply with $4$ to get the result ...
8
votes
0answers
53 views

Solving general (dis)entanglement puzzles

What is the state of the art in (modelling and) solving a general (dis)entanglement puzzle? The following picture shows a nice example: There is a project called "The Untangler", which seems to be ...
5
votes
3answers
84 views

Find a way out in $8 \times 8$ square

Here is one of the mathematic contest problem that my teacher has given me. He said me to solve or find the reason why it cannot be solved. But I was not able to do it. And my searches for similar ...
1
vote
0answers
57 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
vote
2answers
51 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
votes
1answer
57 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
vote
3answers
81 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
30 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
31 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
46 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
127 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
votes
0answers
63 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
votes
2answers
61 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
vote
1answer
34 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
97 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
44 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
79 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
54 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
123 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
167 views

Seeing a pattern (puzzle) [closed]

Does someone see a pattern?: 1 11 21 1211 111221 312211 13112221 1113213211 31131211131221 13211311123113112211 111312211331121321113212221
-2
votes
3answers
58 views

Age puzzle problem [closed]

Can someone help me with the following puzzle problem? I really don't get it: James is two times older than Klaas was when James was as old as Klaas is now, James is 28 years old, how old is ...
1
vote
2answers
84 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
72 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 ...