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
6answers
204 views

Algebra problem stumping me

I have recently run into an algebra problem that goes as follows. Using the digits $1$ to $9$, $$ \left\{ \begin{align} A + B + C + D &= EF \\ E + F + G + H &= CJ \\ B + G + J ...
4
votes
6answers
2k views

Finding the Heavy Coin by weighing twice

Suppose you have $100$ coins. $96$ of them are heavy and $4$ of them are light. Nothing is known regarding the proportion of their weights. You want to find at least one genuine (heavy) coin. You are ...
8
votes
0answers
126 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:...
0
votes
0answers
30 views

Minimum gems required to make a garland containing all permutations, with uniqe colored gems, of size n, where we have infinite gems of N colors.

What is the minimum number of gems required to make a garland (circular) which contains all permutations, with unique colored gems considered as a valid permutation, of size n, when we have infinite ...
1
vote
1answer
51 views

Cars in Traffic [closed]

There is a very long, straight highway with some number of cars (N) placed somewhere along it, randomly. The highway is only one lane, so the cars can’t pass each other. Each car is going in the same ...
2
votes
1answer
59 views

Number of ways of getting from a certain point to another point.

Calculate the number of ways of getting to the pizza without stepping on bombs (you can move up and right) My solution was to calculate the number of ways of getting from the snail to the pizza (...
2
votes
1answer
29 views

Finding the $M^{th}$ person from randomly chosen $S^{th}$ out of $N$ people in a circle?

$N$ people are sitting in a circle, numbered clockwise from $1$ to $N$. Person number $S$ is chosen at random, and we count $M$ people starting from him, and proceeding clockwise, going back to $1$ ...
4
votes
2answers
297 views

What is the minimum number of locks on the cabinet that would satisfy these conditions?

Eleven scientists want to have a cabinet built where they will keep some top secret work. They want multiple locks installed, with keys distributed in such a way that if any six scientists are present ...
0
votes
3answers
277 views

Logic: Door to million dollars

You approach two doors. There are two men. Each man stands in front of one door. Through one door you will win one million dollars. Through the other they will take one million dollars off you. One ...
9
votes
1answer
203 views

Obscuring squares of Rubik's cube

This is a combinatorial question related to Rubik's cube $3\times3\times3$ (and, in the end, its generalizations $n\times n\times n$). I assume that the readers are familiar with this puzzle. Let's ...
2
votes
1answer
95 views

Puzzle: Each entry in a number grid is the average of its neighbors

I'm trying to solve the following puzzle: Each number should be the average of its four neighbors. For example, $x$ should be equal to $\frac{1}{4}(4+10+y+z)$. I don't know how to make a formula ...
19
votes
5answers
522 views

How to arrange these 10 digits to make a correct equation?

My daughter brought home the "problem of the week" last night and it was explained to me as this: Given the following digits: $$1\ \ 1\ \ 2\ \ 3\ \ 3\ \ 4\ \ 5\ \ 6\ \ 6\ \ 7$$ Arrange them ...
1
vote
3answers
65 views

Which box is heavier

There are 2 identical boxes (cubes). First one contains 27 big identical marbles and second one contains 64 small identical marbles. The marbles are made by steel. Supposing that in each box the ...
3
votes
2answers
58 views

Which of these two methods provides the correct answer for this probability riddle?

First, I know this riddle has been asked (many times) before. The question I want answering is why is a tree diagram not a correct method for determining the probability in this case. There are ...
2
votes
0answers
162 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 ...
14
votes
1answer
418 views

Is the solution to this holiday puzzle unique?

I read the following question on internet. this site:(the link is broken now.) Start at 2011. By moving through the maze and doing any arithmetic operations you encounter, exit the maze with a ...
5
votes
2answers
97 views

Logic puzzle: the rich man and the 1000 casks of wine

I recently came across an interesting logic puzzle during a challenge at a programming competition. Neither of the people on the two-person team completing that challenge could figure out an answer ...
0
votes
6answers
15k views

Math Riddle in Combinatorics.

A blind man is on a strange island and he has 2 red pills and 2 white pills, completely identical and has kept in his pockets, he needs to take 1 red pill and 1 white pill order doesn't matter. If he ...
10
votes
3answers
801 views

Come up with some fun “equation Limericks”

We were discussing "Limericks" in my Calculus class. Specifically, "equation Limericks". A Limerick is a poem with five lines. The first, second, and fifth lines should have nine syllables each and ...
3
votes
1answer
101 views

(Green/blue)-eye logic puzzle. Statement validation

There is a logic puzzle aiming on freeing same-color-eyed people from an island. The thing is that they must be certain of their own eye color so that they can leave. For that reason an external party ...
0
votes
2answers
352 views

Mind Teasers : Difficult Brain Twister (Today Challenge)

A strange tradition is followed in an orthodox and undeveloped village. The chief of the village collects taxes from all the males of the village yearly. But it is the method of taking taxes that is ...
6
votes
2answers
100 views

Riddle : Given an integer power, does any integer to this power start with the power?

I initially found the following riddle somewhere : Is there an integer $n$ such that $n^{2004}$ starts (from the left) by $2004$ ? I was unable to find an answer, but I found the question rather ...
0
votes
1answer
42 views

Defective coin weighing problem and ternary representation when number of coins is not a power of 3

We are given $N$ coins and a set of scales. We are told that there is a defective coin and we know whether it is lighter or heavier than the others. Our goal is to identify it in as few weighings as ...
3
votes
1answer
106 views

Explainination of a solved puzzle' solution

This question pertains to the solution of a puzzle offered some times ago here. However, as suggested by the author of the original answer, it might be a good idea to rewrite a more fleshed out ...
1
vote
1answer
149 views

The three-coin-flip riddle

Is the following true (It seems obvious to me that it's not... but... a PhD in physics, Derek Abbott, seems to think others explanation at end of post): Someone flips 3 coins on the table, they are ...
3
votes
1answer
52 views

Generalization of a certain riddle and ultrafilters (?)

I was once told the following riddle: 100 dwarfs stand in a straight line, each wears a hat of the colour red, yellow or green and they can see only the hats of the dwarfs in front of them. A dwarf ...
-1
votes
3answers
48 views

I imagined splitting a powerbill was easy…

Hi guys sorry if there is a really easy way to do this... Our flat got a powerbill and wants to break it up evenly.. The bill is over a 61 day period and the total amount is $343.31 There are six ...
1
vote
2answers
88 views

From a pile of 4 cards, two are drawn.

Just had quite a discussion with my co-workers on this one. If we had a pile of four cards. A King of spades, King of Hearts, Ace of Spades, Ace of Hearts, I pick up two cards and look at them. I ...
2
votes
3answers
103 views

Behind which door is the princess?

Because of Alladin's forbidden love for the king's daughter, he has been sentenced to the usual punishment: death by tiger. As the king is a fair man, he has a fighting chance to escape his doom. He ...
1
vote
1answer
119 views

How to find the no of Questions?

Liz and Mary compete in solving problems. Each of them is given the same list of 100 problems. For any problem, the first of them to solve it gets 4 points, while the second to solve it gets 1 point. ...
1
vote
0answers
62 views

Puzzle: Betting on basketball games strategy

This is a question I saw as an interview question, that I cannot figure out. Devise a method for betting on the individual games of a basketball series so that if your team wins the series, you win \$...
3
votes
1answer
62 views

Sets for which $a_k^2 = \frac{a_1+\ldots+a_n - a_k}{n-1}$

Let $n\geq2$ be an integer. Find all sets $\{a_1,\dots,a_n\}$ of real numbers with the property that for all $k \in \{1,\dots,n\}$: $$a_k^2 = \frac{a_1+\ldots+a_n - a_k}{n-1} .$$ In other words, for ...
1
vote
4answers
12k views

Probability that a leap year has 52 Sundays

For the Question "Find the probability that a leap year has 53 Sundays". The Solution goes : For 53 Sundays, we proceed as: $\frac{366}{7} = 52.28$; So we can be sure that there are 52 Sundays, ...
2
votes
2answers
1k views

Math Puzzle - Fishing

One day 3 men (Ed, Eddie and Eric) decided to go fishing. They agreed that everyone takes one third of the total number N of fish caught. After fishing they went to sleep. At 3:00 AM Ed woke up. He ...
2
votes
2answers
44 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
58 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 ...
2
votes
1answer
69 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:           &...
0
votes
3answers
484 views

Clock puzzle.. Bit tricky

Twin Sisters A and B bought 2 wristwatches at 12 p.m . An Hour later , A's watch reads 1:02 p.m while B's watch reads 12:56 p.m. Later , on same day : If A's watch reads 10 p.m then at that time ...
4
votes
1answer
84 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
528 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 ...
3
votes
1answer
178 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
107 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
51 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
94 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
60 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
137 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
84 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
833 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 _ _ $2$ _ _ $4$ ...
3
votes
1answer
52 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 ...