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
2answers
258 views

Number of Ones Puzzle

$f(n)$ is a function counting all the ones that show up in the sequence $1, 2, 3, ..., n$. IE $f(1)=1$, $f(10)=2$, $f(11)=4$ etc. Discounting the trivial case $f(1) = 1$, when is the first time ...
5
votes
3answers
1k views

Chameleons Riddle

There are 10 red, 11 blue, 12 green chameleons. Sometimes, two chameleons meet. If they are the same color, nothing happens. If they are different colors, they will both change to the third ...
2
votes
1answer
978 views

Logic Puzzle with Eight Clues

I am not sure where to start to solve this problem: Smith, Jones, and Rodriguez are the engineer, brakeman, and fireman on a train, not necessarily in that order. Riding on the train are three ...
6
votes
4answers
264 views

Which sentence among the three sentences is the lie?

The second statement is the lie or the third statement is the lie. This statement is a truth, or the last statement and the second statement cannot both be truths. The first statement is the lie and ...
1
vote
1answer
473 views

Hexagon into 12 identical hexagons

Puzzle: Divide a regular hexagon into 12 identical non-convex hexagons. I found this at Jaap Scherphuis' Tiling Applet, and it looks new to me. Are there any solutions other than the one answer ...
-1
votes
3answers
594 views

Algorithm for finding smallest number in a list, given list of $a$ to $b$

Background Here is a puzzle I have been thinking over. (For some reason I believe there is a linear algorithm for this). Question: You are given list of n numbers and a list of m pairs. You are to ...
0
votes
2answers
217 views

Anti Magic Square

Are the two examples of $4\times 4$ anti-magic squares currently on Wikipedia actually anti-magic squares under the definition given there? The examples are: $$\left[ \begin {array}{cccc} ...
3
votes
2answers
519 views

Rubik's cube puzzle

If we cut along the plane orthogonal to the largest diagonal of a Rubik's cube, what is the maximum number of small cubes can we cut? I thought this should be $9$, but apparently this is not the ...
0
votes
1answer
704 views

Error in the proof of 420 > 422

I came across a puzzle where we need to determine the error in the following proof. False Theorem. 420 > 422 Proof. We will demonstrate this fact geometrically. We begin with a 20 × 21 ...
7
votes
2answers
300 views

Tiling pythagorean triples with minimal polyominoes

Given a Pythagorean triple $(a,b,c)$ satisfying $a^2+b^2=c^2$, how to calculate the least number of polyominoes of total squares $c^2$, needed, such that both the square $c^2$ can be build by piecing ...
0
votes
1answer
216 views

how many of relatives are female

I am working on this problem but I am not so sure my answer is right. The question is below with multiples choices but there is only is right. ...
0
votes
1answer
46 views

If the letters T*(RBJBR)=VPLNT each represented a unique digit, and “RBJBR” was a five digit number, what are possible values for the letters?

If the letters T*(RBJBR)=VPLNT each represented a unique digit, and "RBJBR" was a five digit number, what are possible values for the letters? (Or ONE possible value.) Can we do this in a way that ...
0
votes
1answer
525 views

Create math (addition/subtraction) algorithm for 3 x 3 grid

I'd like to populate a "tic tac toe" board (grid of 3 x 3 squares) with four appropriate entries at which time a user will attempt to solve. I'm having a hard time coming up with a mathematical ...
1
vote
1answer
352 views

Chess Board - Combinatorics

In how many ways you can put three rooks on a chessboard so that no two of them are in same row ,column or diagonal.
1
vote
2answers
121 views

How do you prove that a certain series of moves will guarantee a total win in 'eating apple' math puzzle?

Today our professor presented us with a puzzle of interest called The 'eating apple' problem (I have no idea what is it called formally though). The rules are There are three compartments, ...
4
votes
3answers
2k views

A logic puzzle involving a balance. [duplicate]

Possible Duplicate: Optimal algorithm for finding the odd spheres You have 12 balls and you know that they all weigh the same except for 1 which is heavier or lighter than all the others ...
2
votes
3answers
369 views

A tricky math problem about the difference of 2 squares

Jose is given two 2-digit numbers AB and CD where (A, B, C, and D represent unique digits) and is told to find the difference between the squares of these numbers. However, Jose has dyslexia and ...
3
votes
1answer
246 views

Divisor/multiple game

Two players $A$ and $B$ play the following game: Start with the set $S$ of the first 25 natural numbers: $S=\{1,2,\ldots,25\}$. Player $A$ first picks an even number $x_0$ and removes it from $S$: ...
21
votes
3answers
605 views

Why everytime the final number comes the same?

I have come across an interesting puzzle. Write $20$ numbers. Erase any two number say $x$ and $y$ and and replace with $\text{Number}_{new} = xy/(x + y)$ OR $\text{Number}_{new}= x + y + xy$ ...
-1
votes
1answer
106 views

Is it possible that a person will finds the number what his friend thinks in my mind. the number should between 1-100 via java code

the person will think a number between 1-100. The Questionnaire can ask n number of condition, i.e the number is even or odd, the number is perfect square or prime number, sum of squares etc.
3
votes
1answer
395 views

Mathematics From Futurama

Dear Professor Farnsworth, We at D.O.O.P are trying to mathematically model a rocket ship fueled by your employee Leela's pet Nibbler's pooped Black matter. Obviously this rocket ship is fueled by ...
7
votes
4answers
908 views

Can the product $AB$ be computed using only $+, -,$ and reciprocal operators?

Can the product of $A, B$ be computed using only $+, -,$ and reciprocal operators using a calculator? You can use calculator's memory function (multiply and divide are broken though). Additional: I ...
5
votes
4answers
1k views

Calculating Gröbner basis for Sudoku

I'm trying to write a program that solves sudokus using a Gröbner basis. I introduced 81 variables $x_1$ to $x_{81}$, this is a linearisation of the sudoku board. The space of valid sudokus is ...
1
vote
1answer
930 views

Josephus' Puzzle Basic Java with some basic math.

So I was trying to write a little java program that would solve [Josephus' Problem][1]. The one where you have a certain amount of people in a circle and then a count where every 3rd, 4th or what have ...
2
votes
3answers
315 views

Smallest $k$ s.t. $7x+1=9y+2=11z+3=k$, all positive integers

Find the smallest positive integer, which on dividing with 7 gives remainder 1, on dividing with 9 gives (remainder) 2 and that after division by 11 yields 3 as remainder. i.e., find smallest $k \in ...
2
votes
0answers
83 views

When does $n^2$ divide $2^n+1$? [duplicate]

Possible Duplicate: How many rationals of the form $\large \frac{2^n+1}{n^2}$ are integers? A friend of mine asked me this question over lunch, and it's been a week that I can't do ...
2
votes
1answer
496 views

Having two points of a square and only a compass, how to find the remaining two?

I remember being presented a mathematical puzzle some years back that I still can't solve. The problem is defined as follows: We have two points on a plane, and using only a compass, how do we find ...
8
votes
1answer
303 views

Dividing a square with a hole into two

I was asked the following puzzle for an interview. There is a square sheet. A smaller square hole is made on it (at a random place). How can I divide the rest of the sheet into two halves (in terms ...
18
votes
3answers
3k views

100 prisoners and a lightbulb

100 prisoners are imprisoned in solitary cells. Each cell is windowless and soundproof. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb ...
17
votes
5answers
1k views

Lower bound in algorithmic puzzle

Puzzle: there are $n$ computers most of which are good; the others may be bad ("most" in the strict sense: there are strictly more good computers than bad ones). You may ask any computer $A$ about the ...
10
votes
2answers
1k views

A riddle about guessing hat colours (which is not among the commonly known ones)

This is a riddle I heard recently, and my question is if someone happens to know the solution. I'm asking this out of curiosity more than anything else. So here it is. The riddle is one of the ...
2
votes
2answers
477 views

Jack's birthday riddle

Anytime each of three consecutive months has exactly four Fridays, Jack's birthday will fall in one of those three months. Which month is that?
2
votes
3answers
550 views

Two ants on a triangle puzzle

Last Saturday's Guardian newspaper contained the following puzzle: Two soldier ants start on different vertices of an equilateral triangle. With each move, each ant moves independently and ...
4
votes
2answers
312 views

puzzle about array of numbers

Consider an array of numbers $$ \color{#C00000}{1}\ \hphantom{7\ 6\ 5\ 4\ 7\ 3\ 5\ 7\ 2\ 7\ 5\ 3\ 7\ 4\ 5\ 6\ 7\ }\color{#C00000}{1}\\ 1\ \hphantom{7\ 6\ 5\ 4\ 7\ 3\ 5\ 7\ }\color{#C00000}{2}\ ...
3
votes
1answer
293 views

find all positive integers satisfying $2x^2 - y^{14} = 1$

The following problem was posted to usenet forum de.rec.denksport two weeks ago and no progress was made. Find all positive integers $x$,$y$ satisfying the equation $$2x^2 - y^{14} = 1$$ $(1,1)$ ...
6
votes
2answers
639 views

Optimization Puzzle

You are given a large number of LEGO blocks of size 1. You can build blocks of other sizes using smaller blocks. For example, you can build a block of size 2 using two of size 1 blocks and then build ...
3
votes
2answers
653 views

Strategy / calculus riddle [duplicate]

Possible Duplicate: A lady and a monster Here is another rather famous riddle - I've seen it several times, but only once in its full form that I quote here: A duck is located in the ...
0
votes
1answer
772 views

Using forced perspective to estimate the distance or size of an object

Is it possible to use forced perspective to estimate the distance or size of an object if: Both the top and the bottom of two objects are aligned, the size of both objects are known, but the ...
2
votes
2answers
144 views

Two plants, a rose and a jasmine…

Q1: Two plants, a rose and a jasmine, grow up and around a cylindrical tree trunk. They start from the same point at the foot of the tree, but the rose goes clockwise and the jasmine counterclockwise ...
13
votes
3answers
1k views

Coffee Break Riddle [closed]

Here's a little brain teaser, for your coffe break: $$ 62-63 = 1 $$ Move only one digit to make it right! Have fun!
60
votes
9answers
5k views

100 Soldiers riddle

One of my friends found this riddle. There are 100 soldiers. 85 lose a left leg, 80 lose a right leg, 75 lose a left arm, 70 lose a right arm. What is the minimum number of soldiers losing all ...
1
vote
1answer
180 views

How to express $2012$ in terms of three consecutive primes?

How to express $2012$ in terms of three consecutive primes if you can use each prime number only once ? Source of this problem you can find on this page . Closest number to the $2012$ ...
4
votes
3answers
7k views

Puzzle - 123456789 = 100 with three operations?

Given the sequence 123456789: You can insert three operations ($+$,$-$,$\times$,$/$) into this sequence to make the equation = 100. My question is: is there a way to solve this without brute force? ...
2
votes
0answers
83 views

Is there a use for this technique?

I remember reading once about the following algorithm: Consider a lattice grid and $N$ houses situated at grid points, in which live the town elders. They want to choose a lattice point location ...
2
votes
1answer
658 views

Dot on forehead riddle

A riddle was posted in this mathoverflow question: http://mathoverflow.net/questions/85439/how-does-intuitionism-handle-this-riddle A riddle: You and another person are kidnapped and knocked ...
2
votes
1answer
146 views

Optimal polyomino induced coloring

Which polyominos (with orientation) of $n$ squares, requires the least number of different colors, $c(n)$, such that if this polyomino is placed anywhere on an optimally colored infinite square grid ...
0
votes
1answer
10k views

Puzzle - where did the extra dollar come from? [duplicate]

Possible Duplicate: Riddle (simple arithmetic problem/illusion) I have this small story (sorry about my bad English) : One man (M) took 25 dollar from man (A), and another 25 dollar from ...
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 ...
7
votes
2answers
420 views

Upper bound on minimum number of moves to solve the $m\times n$ sliding puzzle

Define an $m\times n$ sliding puzzle to have an $m\times n$ grid of uniquely numbered squares, and the only valid move is to swap the special square numbered 0 with an orthogonally adjacent ...
165
votes
3answers
7k views

How many fours are needed to represent numbers up to $N$?

The goal of the four fours puzzle is to represent each natural number using four copies of the digit $4$ and common mathematical symbols. For example, $165=(\sqrt{4} + \sqrt{\sqrt{{\sqrt{4^{4!}}}}}) ...