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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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 ...
19
votes
3answers
527 views

Making $121$ with five $0$s

So I say this puzzle online a few days ago and found it quite interesting. The original question was Make $120$ using only five $0$s. Well, I said to myself, this is utterly trivial. Note that ...
4
votes
3answers
10k views

Missing dollar problem

This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw. You see a top you want to buy for $\$97$, but you don't have any money so you ...
3
votes
1answer
175 views

Diophantus' Lifespan

Today I saw Diophantus' Epitaph. For those of you who don't know it and don't feel like googling: 'Here lies Diophantus,' the wonder behold. Through art algebraic, the stone tells how old: 'God ...
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 ...
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\\...
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
118 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 ...
17
votes
1answer
2k views

New Year's eve riddle

A bit more than 20 years ago, the following exercise was assigned to a class as the christmas holiday exercise. I did search for a while whether it was posted here earlier and could not find it. I ...
1
vote
1answer
812 views

How many $3$ digit even numbers can be formed by using digits $1,2,3,4,5,6,7$, if no digits are repeated?

How many $3$ digit even numbers can be formed by using digits $1,2,3,4,5,6,7$, if no digits are repeated? ATTEMPT There are three places to be filled in _ _ _ I wrote it like this _ _ $2$ _ _ $4$ ...
5
votes
2answers
9k 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 $9$ o'...
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 ...
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 ...
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 ...
8
votes
7answers
4k views

The number of bottles of beer one can buy with $10, after exchanging bottles and caps [closed]

My answer to this question is 15, but my dad insists I am wrong. Who is right? $2 can buy 1 bottle of beer. 4 bottle caps can be exchanged for 1 bottle beer. 2 empty bottles can be exchanged ...
27
votes
5answers
403k views

How many squares actually ARE in this picture? Is this a trick question with no right answer?

This is one of those popular pictures on sites like Facebook. I always see a huge variation of answers such as $8, 9, 16, 17, 24, 28, 30, 40, 41, 52,$ etc., yet I've never seen a definitive answer on ...
0
votes
0answers
59 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 ...
1
vote
3answers
471 views

Algebraic solution to the Broken Weight Problem

Here is a problem I was sent, which it turns out was first posed by Claude Gaspard Bachet de Méziriac in a book of arithmetic problems. The problem is as follows: A few years ago, a King's ...
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 ...
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?
14
votes
1answer
2k views

After swapping the positions of the hour and the minute hand, when will a clock still give a valid time?

At 12 o'clock, the hour hand and minute hand of the clock can be swapped, and the clock still gives the same time, but at 6 o'clock, it can not be swapped. So in what cases when we swap the hour and ...
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 ...
0
votes
2answers
107 views

A man returns home from a two month trip and discovers that his enemies have put a moat around his property.

A man returns home from a two month trip and discovers that his enemies have put a moat around his property. The property consists of a 108×108 foot square centered within a 140×140 foot square, and ...
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 ...
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 ...
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 ...
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, ...
4
votes
4answers
3k views

How to calculate the number of pieces in the border of a puzzle?

Is there any way to calculate how many border-pieces a puzzle has, without knowing its width-height ratio? I guess it's not even possible, but I am trying to be sure about it. Thanks for your help! ...
4
votes
4answers
7k views

What is the name of the logical puzzle, where one always lies and another always tells the truth?

So i was solving exercises in propositional logic lately and stumbled upon a puzzle, that goes like this: Each inhabitant of a remote village always tells the truth or always lies. A villager will ...
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 $xyz$?
1
vote
5answers
5k views

Find a possible pair of numbers given HCF and a factor of the LCM

I was just going through a GCSE paper with a student and I came across a question that I'm struggling to find a good method for. The question was this: Martin thinks of two numbers. The ...
2
votes
3answers
74 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 ...
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?
5
votes
1answer
3k 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, ...
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 ...
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
109 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 $5!$
0
votes
4answers
112 views

Problem related to a given diagram

I came across the above problem but do not know how to tackle it. Can someone point me in the right direction? Thanks in advance for your time.
11
votes
9answers
653 views

Make the number $100$ out of $1,2,3,$ and $4$ digits, without repeats

How can we make the number $100$, using only the following digits: $1,2,3,4$. You cannot repeat any of them.