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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18
votes
5answers
4k views

Tiling pentominoes into a 5x5x5 cube

I have this wooden puzzle composed of 25 y-shaped pentominoes, where the objective is to assemble them into a 5x5x5 cube. After spending quite a few hours unsuccessfully trying to solve the puzzle, I ...
1
vote
1answer
15 views

Voting with 3-way ties

From Peter Winkler's 'Mathematical puzzles' Ashford,Baxter and Campbell run for election and end up in a 3-way tie. To break it, they solicit voters' second preference and there is also a 3-way tie. ...
3
votes
2answers
32 views

Which functions can be obtained by applying these syntactic rules?

Here's an intentionally weird question for ye all. Start off with the expression $x$. Rule 0. We're allowed get a new expression from an old expression by replacing a subexpression with an $\mathbb{...
2
votes
2answers
386 views

Number of songs sung.

There were 750 people when the first song was sung. After each song, 50 people are leaving the hall. How many songs are sung to make them zero? The answer is 16, I am unable to understand it. I am ...
0
votes
1answer
27 views

Finding formula [on hold]

X Y Z Answer 8 2 4 0.5 8 2 2 0 8 2 8 1 My professor gave this as a sort of riddle to figure out, and it's ...
0
votes
1answer
28 views

infinite square grid of resistors

Given an infinite, 2-d, square grid of 1 Ohm resistors, what is the resistance between two adjacent nodes? (Something like a very large window screen, where the wires have finite resistance, but no ...
3
votes
2answers
117 views

Math Snake Puzzle

A colleague recently showed me the following puzzle game and I'm interested in how this can be solved. I thought it would be a good talking point for you guys as well :) A detailed description of ...
-2
votes
0answers
40 views

Next number in the sequence 19, 10,11, 18, 38,? [on hold]

What is the next number in the sequence 19, 10, 11, 18, 38 ? I received this image in a WhatsApp group. I don't know the book from which it is taken. It is question 140 of the image
0
votes
1answer
46 views

Work and efficiency puzzle

There are $2$ people $A$ and $B$. $A$ requires $a\;$ days to complete certain amount of work and $B$ requires $b\;$ days to complete the same amount of work. If $A$ begins the work a day before $B$ ...
-5
votes
1answer
57 views

What would be the solution to this logic puzzle? [closed]

This is the puzzle I am having trouble in understanding Also, do explain me the question along with the answer. Thank You
4
votes
4answers
365 views

Find the sum of angles without trigonometry?

I have found the sum it's $180$ but using right triangle and sine theorem.
0
votes
0answers
31 views

Maximum length sequence with negative and positive subsequences

From ' mathematical puzzles' By Peter Winkler: " At the stockholders' meeting the CEO presents month-by-month profits and losses and declares : ' Since the last meeting we have made a profit in ...
10
votes
2answers
152 views

5x5 Bingo Puzzle [Logical thinking problem]

5 people participate in a custom game. They are given blank cards, in which they have to fill numbers from 1-25 in a 5x5 table. Each card must contain all the numbers from 1-25 without repetition. The ...
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?
0
votes
1answer
50 views

A cool number-theoretic puzzle in IMAT: find the last digit

This test is from IMAT 2015 (International Medical Admission Test): When I made a hotel reservation online yesterday I was given an $8$ digit booking reference which contained no zeros. It did, ...
4
votes
2answers
127 views

Find $I$ in $\frac{\overline{SIX}}{\overline{NINE}}=\frac23$

In $\frac{\overline{SIX}}{\overline{NINE}}=\frac23$ every letter denotes a UNIQUE digit,find $I$. Expanding the fraction in base $10$ we have: $300S+30I+3X=2020N+200I+2E$ , but this doesn't ...
2
votes
6answers
3k views

Proof that a common brain teaser is wrong (Burning Rope)

There is a common brain teaser that goes like this: You are given two ropes and a lighter. This is the only equipment you can use. You are told that each of the two ropes has the following property: ...
25
votes
3answers
760 views

Sudoku with special properties

Sudoku is a puzzle, with the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid (also "sudoku-blocks") contains all of ...
13
votes
1answer
592 views

Cookie Clicker Chocolate Egg strategy

Introduction Cookie Clicker is a silly Javascript based web game. Here is a brief description of what you do: (description taken from this question: Explain a surprisingly simple optimization result) ...
2
votes
1answer
64 views

Circle Puzzle Geometry

Two friends are playing a game. One friend stands in the middle of a circle radius 100m. His objective is to leave the circle. He may take one step at a time, distance 1m, in any direction. However, ...
4
votes
1answer
91 views

Mathematical puzzle on the coordinate planes.

Recently, I come across this quite interesting mathematical puzzle: Consider the ten points $(0,0)$, $(1,2)$, $(3,3)$, $(4,1)$ and $A, B, C, D, E, F$ on the coordinate plane. It is known that if any ...
20
votes
6answers
711 views

Non-trivial “I know what number you're thinking of”

Consider the following 'trick' (WARNING: very lame) Think of a number. Multiply this number by two. Add four. Divide the number by two. Subtract the number you were originally thinking of. I guess ...
1
vote
2answers
70 views

Nice explanation for simple puzzle

There is a simple game with coins that goes as follows. You have $x$ coins and two players who take turns. Each player can either remove one or two coins. The winner is the person who removes the ...
0
votes
1answer
21 views

Devising an $n$-place mastermind variation algorithm

A few days ago I came across such a problem at the contest my uni was holding: Given the history of guesses in a mastermind game using digits instead of colors in a form of pairs $(x, y)$ where $...
4
votes
1answer
995 views

Prove that there is only one way to make a square using all six tangram pieces

I am pretty sure there is only one way to make a square from the six tangram pieces: How can I prove this is the only way respecting all symmetries?
3
votes
1answer
40 views

How to tame a Rechenschlange

I found the following problem, called Rechenschlange (literal translation: calculation snake) in a German puzzle calendar: Fill the blanks with the numbers 1-9. Each number must only appear once. ...
12
votes
1answer
232 views

Doing a magic trick with limited memory (from a problem solving course)

I got the following question in a problem solving course: There are four different objects lying on places 1, 2, 3, 4. A magician closes his eyes and someone from the audience comes. He switches ...
-1
votes
2answers
109 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 ...
4
votes
2answers
49 views

55 Coins- / Young-Diagram Rearrangment-Riddle

this has been a riddle to difficult for me to understand the solution some year ago. Even though the riddle seems really easy. You have got 55 coins. Someone builds an arbitrary number m of stacks ...
3
votes
2answers
96 views

2048 Logic Puzzle

I thought up this logic problem related to the 2048 game. If all 16 tiles on a 2048 board all had the value 1024, how many ways are there to get to the 2048 tile? Here is what I am talking about in an ...
16
votes
4answers
2k views

9 pirates have to divide 1000 coins…

A band of 9 pirates have just finished their latest conquest - looting, killing and sinking a ship. The loot amounts to 1000 gold coins. Arriving on a deserted island, they now have to split up the ...
-1
votes
2answers
84 views

Math's puzzle school problem

I got this weird homework situation and i can't find out what the answer is. I got to find out how to get $828$ using the numbers $8, 6, 8, 3, 75$ and $9$. Moreover, I can use all the operators $*, -,...
21
votes
5answers
16k views

How is this a number sequence $58, 26, 16, 14, 10$

I recently had a IQ Test taken and we all got stuck on the same question. The question was: What comes next in the following sequence? $$58, 26, 16, 14,\_\_$$ The answer given in the answer sheet ...
3
votes
2answers
219 views

Game between 2014 card players where everyone with at least 2 cards passes a card to each of his neighbors

2014 card players sit around a big table. One of the players begins with 2014 cards on his hand, and the other have none. The rules for the game are: Every minute shall every player, who has 2 ...
-1
votes
1answer
31 views

Two guys pick from $n$ stones, the numbers of stones they can pick lie in a given set S. When the guy who pick first will win?

Alice and Bob take turns to pick stones from a pile of $n$ stones. Each number of stones they pick must lie in a given finite set $S\subset \mathbb{N}$. Who cannot pick will lose. If Alice picks first,...
1
vote
1answer
45 views

finding the missing number by pattern

In this riddle you need to find a pattern between every couple of numbers. Given numbers $5$ and $10$ there is a pattern like in the numbers $10$ and $3$. Given numbers $10$ and $15$ there is a ...
1
vote
1answer
35 views

Create a strictly increasing sequence following criterias

Problem Let y be a sequence of real numbers (of length $n$) bounded in the range [0,1]. I am trying to calculate the sequence x ...
0
votes
2answers
38 views

Do these infinite expressions have a meaning?

While playing with expressions, I came up to the following "infinite sums". I haven't seen them anywhere else but maybe I didn't look long enough. Find the values of $s$ and $t$. $$s=\sum\nolimits_{1}^...
23
votes
1answer
555 views

Finding real money on an even stranger weighing device

You have $n$ coins which each weigh either $20$ grams or $10$ grams. Each is labelled from $0$ to $n-1$ so you can tell the coins apart. You have one weighing device as well. At the first turn you ...
4
votes
2answers
57 views

Meeting probability of two bankers: uniform distribution puzzle

Two bankers each arrive at the station at some random time between 5PM and 6PM (arrival time for each of them is uniformly distributed). They stay exactly five minutes and then leave. What is the ...
4
votes
7answers
146 views

A logic riddle from “The Lady or the Tiger?” by Raymond Smullyan

Just to clarify, Case 3 and Case 4 must have flawed reasoning in order to reconcile my proof with the author's. I have been having a problem with a particular riddle from Raymond Smullyan and I can't ...
6
votes
1answer
233 views

Why was I wrong about the monster-gem riddler

Every week I like to do the fivethirtyeight.com Riddler, an interesting and pleasantly challenging (at least for me) weekly math puzzle which comes out Fridays, with the answer and explanation to the ...
52
votes
10answers
23k views

Taking Seats on a Plane

This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless Imagine there are a 100 people in line to ...
2
votes
2answers
42 views

Awesome riddle including independence and exponential distribution [closed]

The life cycles of 3 devices $A, B$ and $C$ are independent and exponentially distributed with parameters $\alpha,\beta,\gamma$. These three devices form a system that fails if not only device A fails ...
1
vote
0answers
75 views

Cat and a mouse on a circle

I hope this is the right plcae to post it as I'm not sure if the solution is mathematical. I saw this riddle on a board at the university and it seems that there's something I'm missing. It goes as ...
0
votes
1answer
57 views

Proof of coin and bag problem

There are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively ...
2
votes
2answers
934 views

Sudoku Puzzles and Propositional Logic

I am currently reading about how to solve Sudoku puzzles using propositional logic. More specific, they use the compound statement $\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$, ...
2
votes
2answers
888 views

Basic probability : the frog riddle - what are the chances?

A few days ago I was watching this video The frog riddle and I have been thinking a lot about this riddle. In this riddle you are poisoned and need to lick a female frog to survive. There are 2 frogs ...
2
votes
4answers
1k views

the time at which the hour & minute hands in a clock becomes straight?

At what time exactly does the minute hand and the hour hand in a clock becomes straight between 7O'clock & 8O'clock. Iam getting the time is in between 7:05 and 7:10 but what after that. can it be ...