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
2answers
43 views

how many cubes have at least $1,2,3$ colors on them

I have a painted cube, which is cut into $n^3$ smaller cubes. I now want to find the number of cubes which have $1$,$2$,$3$ sides painted. I know the long way round of taking each cube and putting ...
1
vote
1answer
55 views

Is it possible for this puzzle to be solved without the use of computational software?

This puzzle was found from the Hot Network Questions on the right. A repost of a question in a way (from Mathematica SE), but I was wondering if the following puzzle could be done: A quick ...
3
votes
4answers
181 views

Multiplication without figures

I have taken the 12th problem of this pdf, do you know any way to resolve it without using brute force? Simply I have to replace '*' of this multiplication below with correct digits, in order to have ...
4
votes
1answer
80 views

A bird flies between two cars infinite times [duplicate]

The following question and answer is taken from careerbless A naughty bird is sitting on top of the car. It sees another car approaching it at a distance of 12 km. The speed of the two cars is ...
8
votes
0answers
122 views

Limit approximation for $\pi$ in the four fours puzzle?

The four fours puzzle is a recreational math puzzle whose aim is to express whole numbers using four occurrences of the digit 4 and a specified set of operators. A common variety permits the following:...
1
vote
2answers
106 views

The Triple Number Game (n + n + n)

I work at the Science Museum on weekends, and I sometimes present the following puzzle: $$0\;0 \; 0 = 6$$ $$1 \; 1 \; 1 = 6$$ $$2 \; 2 \; 2 = 6$$ $$3 \;3 \; 3 = 6$$ $$\vdots$$ $$n\;n\;n=6$$ The idea ...
-1
votes
2answers
49 views

How to solve this riddle mathematically? [closed]

Its a classic puzzle. It is as follows- You have died and you are in afterlife. You have two doors in front of you. One leads to heaven and the other leads to hell. One guard is guarding each gate. ...
1
vote
1answer
90 views

Each alphabet of KANGAROO is replaced with number by $2$ people; which alphabet is replaced with the same number?

In the word KANGAROO Bill and Bob replace the letters by digits, so that the resulting numbers are multiples of $11$. They each replace different letters by different digits and the same letters by ...
1
vote
1answer
59 views

$4\times ABCDE = EDCBA$: Four times a five digit integer is that integer backwards.

A student gave me this puzzle the other day. Where $A,B,C,D,E$ are distinct digits, and where $A,E\ne0$, what 5 digit integer satisfies the condition below? $$4\times ABCDE=EDCBA$$ What I'm ...
2
votes
1answer
117 views

Math riddle: reach sum of 100 with numbers $0…9$

This is a riddle my friend gave me and we don't know the answer so we would like some help. The task is to use all of the numbers $0,1,2,...,9$ once each to get a sum of $100$ only using the plus sign....
1
vote
1answer
79 views

Puzzle. Transfer maximal coal using a train [duplicate]

We need to transfer coal from point $A$ to point $B$ using a train. There is $9000$ tonne at point $A$. The distance between point $A$ and $B$ is $3000$ km. Train can carry only $3000$ tonne included ...
3
votes
1answer
53 views

Minimum number of squares required in grid so that the next square added is not isolated

Given a rectangular grid with $n$ rows and $m$ columns in which squares may be placed, what are minimum number of squares required so that the next square added cannot be placed in isolation? ...
-3
votes
1answer
61 views

Counting and Abstract Problem Solving [closed]

Suppose that you have a bucket holds fiv-sev c, and one holds tw-one c. How could you use them to measure out thre c of water?
1
vote
2answers
53 views

Connecting up boxes mathematically (Puzzle)

How would you connect each black box once to each colored box without any lines overlapping, this is racking my brain so please help. Note that you can move the boxes where ever you want. Maybe ...
3
votes
1answer
51 views

Number bag riddle — minimal solution?

The riddle: Consider $N$ different bags $B_1$ to $B_N$. Each bag may be filled with numbers. Can you fill these bags with numbers from $1$ to $N$ so that the following conditions hold? 1) $n \in ...
0
votes
0answers
58 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 ...
23
votes
3answers
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\\...
2
votes
2answers
76 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?
2
votes
5answers
4k 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?
42
votes
4answers
6k 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
123 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
44 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
73 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
73 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
1answer
39 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
32 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
54 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
72 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
88 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
164 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
31 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 ...
3
votes
2answers
156 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
49 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
19 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
18 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
108 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
513 views

Solve carefully [closed]

Solve carefully ... $$25-55+(85+65)=$$ You probably won't believe it, But this equals $5!$
2
votes
0answers
150 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
50 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, ...
14
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 ...
9
votes
0answers
72 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
99 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
1answer
66 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
68 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
74 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
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
34 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
52 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
135 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 ...