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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5
votes
3answers
234 views

What is the value of D here?

Number $S$ is obtained by squaring the sum of digits of a two digit number $D$. If the difference between $S$ and $D$ is $27$, then the two digit number $D$ is? My thoughts: Let the two digit number ...
1
vote
1answer
136 views

Explanation for a peculiar property of a number

I had come across a problem, where 2 people play a game where think of a number n, and turn by turn subtract a number $p$ from $n$ where $p$ is a prime and is $p < n$ and 1 is taken as prime here. ...
7
votes
2answers
894 views

Find missing number from sum of first few natural numbers

A child was asked to add the first few natural numbers $1+2+3+...$ as long as his patience permitted. As he stopped, he gave the sum as $575$. When the teacher declared the result wrong, the child ...
2
votes
1answer
249 views

Dissection of a chess board into 4 congruent pieces

Consider a standard $8\times 8$ chessboard where a pawn is placed on each of the squares $d1,d2,d3,d4$ . Dissect the board into $4$ congruent pieces (reflections are allowed) such that each piece ...
0
votes
1answer
46 views

Find out the length of a recurrence

I have this rules for creating a list of numbers: $x/2$ if $x$ is even, repeat $3x+1$ if $x$ is odd, repeat if $x=1$, stop so for example, starting from 15, the list will be: 15, 46, 23, 70, 45, ...
1
vote
4answers
3k views

Escalator puzzle equation

I'm trying to understand the escalator puzzle. A man visits a shopping mall almost every day and he walks up an up-going escalator that connects the ground and the first floor. If he walks up ...
0
votes
4answers
405 views

A logic puzzle from TES: Arena

Its nice when games have riddles hidden in them. While playing TES:Arena, I came across an unusual logical puzzle: There are 3 cells. If Cell 3 holds worthless brass, Cell 2 holds the gold key. If ...
3
votes
2answers
227 views

What area of mathematics is this problem asking about?

A colleague posted this on a whiteboard (as a brain-teaser I guess): A $\rightarrow$ B; B $\rightarrow$ C; AD $\rightarrow$ E; BE $\rightarrow$ C; BF $\rightarrow$ D; AC $\rightarrow$ F What is ...
0
votes
4answers
321 views

Can you help me solve these questions related to a Logical theory?

In a group of 200 people, number of people having at least primary education (assuming - Category I): number of people having at least middle school education (Category II): number of people having ...
2
votes
1answer
1k views

In how many ways ( using only whole numbers ) can we divide 49 into 6 parts so that we can obtain any number between 1 to 49?

The series which forms the basis of all the other series is:- 1,2,4,8,16,18. Some other combinations are:- 1,2,3,7,14,22 ; 1,2,4,7,15,20 ; 1,2,4,8,13,21. However, I obtained the basic combination by ...
5
votes
3answers
305 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
20
votes
1answer
1k views

The $n$ Immortals problem.

I saw this riddle posted on reddit a long time ago, called the "Seven Immortals." In the beginning, the world is inhabited by seven immortals, ageless and sexless, who begin to multiply and ...
2
votes
2answers
712 views

Divide $40$ to $4$ parts such that every number from $1-40$ can be realized

How can you divide $40$ to $4$ parts such that every number from $1-40$ can be realized just by adding or subtracting those $4$ parts?
7
votes
4answers
300 views

A math teacher thought of a positive integer of two digits.

A math teacher thought of a positive integer of two digits. She wants her two intelligent students Hanna and Charlie determine the exact number thought. For this, Hanna is privately told how many ...
3
votes
1answer
137 views

Monty Hall Application

Driver A comes to a 3 way path junction but is not sure which one to take. Just as he decides to take path 1, a cyclist came by and told driver A all he knows is that he is going on path 3 which would ...
3
votes
2answers
367 views

What are good methods for solving Conway's card-stacking puzzle?

Suppose there is a table with three marked spots, $A, B, $ and $C$, on which playing cards can be put, face up. Initially, an ace (1), a deuce (2), and a trey (3) are placed on one or more of these ...
0
votes
4answers
135 views

Is there a theorem that disproves this or is this just some made up meaningless thing?

I find this slightly funny. I saw this on a meme:$$\begin{align}a=x\\ a+a=a+x\\ 2a=a+x\\ 2a-2x=a+x-2x\\ 2(a-x)=a+x-2x\\ 2(a-x)=a-x\\ 2=1\end{align}$$ How can these strange algebraic manipulations not ...
2
votes
4answers
394 views

Monty Hall problem vs. roulette systems - how are they different?

So I got interested in the Monty Hall problem - I understand what it's about, but somehow I can't wrap my head around the idea of the final choice not being 50/50. More precisely: we all know (or ...
2
votes
3answers
688 views

Use three 11's and various math symbols to make an equation equal to 6

The puzzle is to use the following symbols $$+,\;-,\;*,\;/,\;(\;,\;),\;!, \;\sqrt(\cdot)$$ in order to make a valid equation out of $$11~~~~~~11~~~~~~~11 = 6.$$ (There are three elevens with space in ...
2
votes
2answers
103 views

Tower of dice - Abstracting a practical problem to a mathematical method

This question arose when playing yahtzee with some friends. Not entirely sure if I'm in the right area, but hope you can help. How many dice do you need to create a tower whose walls have the same ...
2
votes
4answers
597 views

balance scale problem for 13 (not 12) items

The 12-item balance scale puzzle is very familiar. The object is to find the lone non-standard item (if one exists) out of a group of 12 seemingly identical items, using a balance scale and a maximum ...
18
votes
7answers
1k views

“How long 'til we get there?” Road trip puzzle

Road trips can be fun, but they often appear to go slower the closer you get to your destination. I thought up this puzzle while on a recent trip. Thought it would be good food for thought. Curious ...
5
votes
5answers
441 views

Puzzle: Dropping balls along the way

A man has some balls in his pocket. Let the number of balls in his pocket be $n$.(Consider $n$ as an integer. If any decimal value occurs, consider its floor value. For example, if $n$ = 2.6 then take ...
6
votes
0answers
143 views

Card passing game, maximum length

Quoting from this question: There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two ...
3
votes
4answers
407 views

Numerical puzzle

I'm stuck here with some numerical rebus - Given: $A^2=BC, A^3=CA$ Find: $A+B+C$ $13$ $12$ $11$ $10$ (only one correct solution) Note that letters represent digits. I can't think of any idea ...
2
votes
2answers
340 views

Numerical rebus

Given: ${AA}\times{BC}=BDDB$ Find $BDDB$: $1221$ $3663$ $4884$ $2112$ The way I solved it: First step - expansion & dividing by constant ($11$): $AA\times{BC}$=$11A\times{BC}$ $1221$ => ...
4
votes
2answers
290 views

Cut the rope puzzle

This question was asked to me in an interview, I still cannot think of its solution. Can anyone help? Following is the question: Given an infinite number of ropes of length $R$, you have to ...
0
votes
3answers
638 views

knight and knave problem

For this question, suppose you are on the island of knights and knaves. Remember that knights always speak truth while knaves always tell a lie. (a) Suppose you come across two of the natives. You ask ...
16
votes
1answer
1k views

Given a set of digits, what is the biggest number we can make using exponentiation - numberphile noodle quiz

The question is motivated by a question on a can of number noodles. Each item is a digit between $0$ and $9$. Clearly, if you form a string and consider it to represent a base $10$ integer, then ...
2
votes
2answers
308 views

Prove or disprove a chessboard with diagonal corners removed, cannot be tiled with L shape pieces or size 2

I think this is impossible, but I don't know how to prove an integer solution doesn't exist for a given equation. Here's my approach: First, observations: The removed tile will be of the same color. ...
3
votes
2answers
325 views

A less challenging trivia problem

There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two cards. At a signal, each person ...
-3
votes
2answers
155 views

Find the last number in the given sequence

Find the last number in the given sequence $$\begin{pmatrix} 4& 9& 20\\ 8& 5& 14\\ 10& 3& ?\end{pmatrix}$$ (It's $3\times3$ matrix)
2
votes
1answer
538 views

Puzzle on the triangle.

In triangle top four figures that have to be repositioned to form the "triangle" without a unit square. How to explain this? Thank's.
8
votes
3answers
203 views

Group of sphere transformations, impressing friends

Ok, so here's the story: I am reading a book on algebra and, via some exercises, discovered that in any group $G$, the order of $x \cdot y$, written $o(x \cdot y)$, equals $o(y \cdot x)$. Now, this is ...
25
votes
7answers
6k views

Is there no solution to the blue-eyed islander puzzle?

Text below copied from here The Blue-Eyed Islander problem is one of my favorites. You can read about it here on Terry Tao's website, along with some discussion. I'll copy the problem here as ...
2
votes
2answers
347 views

Four men seated in a boat puzzle

I am looking for an elegant way to solve this rather simple logic puzzle using mathematical logic (statements, conjunctions, disjunctions, implications, tautologies, predicate logic and so on). I am ...
6
votes
1answer
931 views

Find volume of crossed cylinders without calculus.

I found this puzzle here. (It's labeled "crossed cylinders".) Here's the description: Two cylinders of equal radius are intersected at right angles as shown at left. Find the volume of the ...
6
votes
2answers
1k views

topology puzzle - without cut the rope, separate two rings

hello I wonder whether this puzzle is possible to solve. if possible, what kind of thing should I learn to solve this? the problem is make left one to right one without cut the rope only stretch and ...
0
votes
1answer
58 views

homework cheyenne

It is a four-digit number. Its largest place value is its one place. The squares of each of its digits are less than nine. Its thousandths didgit divided by its ones digits is 50%. The sum of two pf ...
0
votes
1answer
882 views

three girls gave a friend 60 rupees and asked her to buy them a kilo of mangoes from the market. [duplicate]

Possible Duplicate: Riddle (simple arithmetic problem/illusion) three girls have a friend 60 rupees and asked her to buy them a kilo of mangoes each from the market. the mangoes cost 55 ...
1
vote
1answer
278 views

Setting A Paper on Mathematical Puzzles

I need to set a paper for High School Students on Mathematical Puzzles which make the use of logic, simple combinatorics and algebra. Can people provide new and innovative questions. The questions ...
6
votes
1answer
395 views

“8 Dice arranged as a Cube” Face-Sum Problem

I found this here: Sum Problem Given eight dice. Build a $2\times 2\times2$ cube, so that the sum of the points on each side is the same. $\hskip2.7in$ Here is one of 20 736 ...
7
votes
2answers
3k views

Father and daughter river crossing puzzle.

There are 3 men and 3 girls. lets name them ABC, A's daughter X, B's Daughter Y, C's daughter Z. Rule to cross the river: At once Only two Can go on boat. Only Men know how to drive the boat (So ...
2
votes
1answer
127 views

Books in the Library of Babel

I recently came upon a comment in the mathematics overflow stating that the infinite string of pi was similar to The Library of Babel. This library is a universe containing every possible combination ...
2
votes
2answers
142 views

Puzzle on Ranks

Here is a puzzle from textbook : 40 Puzzles and Problems in Probability and Mathematical Statistics Peter draws n = 100 independent realizations of a continuous rv and ranks them in increasing order ...
4
votes
1answer
188 views

What function does this infinite series represent?

$$\frac14+\frac{x-4}{2!x^2}-\frac{(x-4)(2x-4)(3x-4)}{4!x^4}+\frac{(x-4)(2x-4)(3x-4)(4x-4)(5x-4)}{6!x^6}\mp\ldots$$ Can anyone deduce the sum of this series? The reason I ask is because I made it and ...
1
vote
1answer
178 views

Winning single-pile, variable limits Nim [duplicate]

Possible Duplicate: Winning strategy for a matchstick game The rules of this variant of Nim are as follows: Starting at zero, each player counts up between 1-N numbers. The person that ...
1
vote
1answer
3k views

How Old Are Children?

Two old friends, Jack and Bill, meet after a long time. Jack: Hey, how are you man? Bill: Not bad, got married and I have three kids now. Jack: That’s awesome. How old are they? Bill: The product of ...
8
votes
3answers
1k views

How Strong is an Egg?

You have two identical eggs. Standing in front of a 100 floor building, you wonder what is the maximum number of floors from which the egg can be dropped without breaking it. What is the minimum ...
0
votes
1answer
59 views

Deduction from a sequence of statements

check the validity of the following argument: "if the rents of hotels in jammu are fixed or the prices of the commodities are reduced then the income of bussinessmen shall decrease. If the income of ...