Questions tagged [algebra]
A mathematical puzzle about the manipulation and solution of equations. Use with [mathematics]
66
questions
7
votes
2
answers
810
views
Vector Sum of Pythagorean Triples
Given any finite set of linearly independent Pythagorean Triples, show that the vector sum of this set is never a Pythagorean triple.
- 519
3
votes
0
answers
186
views
Perfect 9-sided die [closed]
I am working on a fair 9-sided die and I settled on a design where you select three edges of a cube where the two sides that one edge touches don't overlap with any of the other sides touched by the ...
- 31
2
votes
2
answers
178
views
A bear of a different colour [duplicate]
Here is a stunning new version of the famous bear problem. IT IS NOT A DUPLICATE, OR LATERAL THINKING. MATHEMATICS REQUIRED.
A photographer stepped out of their tent with a camera and walked:
1 km ...
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6
votes
2
answers
733
views
Balancing the marble game (Red marbles are OP, please nerf)
Ash and Bree are playing a simple game of chance:
They fill a bag with small marbles coloured red or blue.
They take turns to draw a marble from the bag without looking, then:
If Ash draws a red ...
- 3,616
2
votes
1
answer
270
views
Puzzle regarding emptying of cup!
Initially, I have $3$ cups with infinite capacity and some prefilled amount of water(positive integers). I can do only one operation repeatedly by choosing any $2$ out of $3$. The operation is that if ...
- 125
5
votes
2
answers
181
views
Highest n where an equal number in all cells is (im)possible
Inspired by Board with all 2020s :
Zeroes are written in all cells of a n×n board. We can take an arbitrary cell and increase by 1 the number in this cell and all cells having a common side with it.
...
- 8,000
18
votes
5
answers
1k
views
Board with all 2020s
Zeroes are written in all cells of a $5 \times 5$ board. We can take an arbitrary cell and increase by 1 the number in this cell and all cells having a common side with it. Is it possible to obtain ...
- 880
2
votes
3
answers
350
views
Can you minimise the arithmetic average?
Let $n$ be a positive integer. There are $2n$ $1$s written on the whiteboard. John repeats the following procedure $3n$ times, as follows:
Choose two numbers $x,y$ on the board, then replace each of ...
- 5,560
-5
votes
1
answer
172
views
You went to the casino again [closed]
You went to the casino again and saw a cardboard, with the following written on it:
There are $\color{brown}{\text{dirt}}$ coins. Every time, you pay \$$10$. Then the coins will be thrown, and you ...
- 5,560
12
votes
4
answers
786
views
A packing game!
Amy and Ben are playing a game which is suggested by a genie. Amy first chooses $a,b,c\in\mathbb{R}^+$. Then a empty cuboid box with internal measurements $a+b,b+c,c+a$, and infinite supply of cuboid ...
- 5,560
3
votes
2
answers
215
views
Count the squares [closed]
My professor at college loves geometry and discrete mathematics.
He gave us a question let see if you can solve it.
He asked us
...
3
votes
2
answers
220
views
Cube the digits and carry on
Take a number between 2001 and 2100 inclusive. Cube the digits of the number and add them together, then repeat the process with the new sum and restart the process over and over. For example if I ...
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1
vote
2
answers
156
views
Solve the magic square
My friend gave me the following magic square to solve
$$\begin{bmatrix}\frac23&5&?\\\frac19&?&?\\?&?&?\end{bmatrix}$$
I can solve it. Can you?
You must provide logical ...
- 5,560
9
votes
1
answer
445
views
Whose birthday is it?
A group of people have gathered for a birthday celebration. Their ages are related as follows:
The product of the 1st person's and the 2nd person's ages is $311\frac{2}{3}$ plus the 3rd person's age.
...
- 418
6
votes
2
answers
632
views
Can you find the number?
There's a number with the following characteristics:
The hundreds digit plus the units digit minus the tens digit equals 8.
3 times the hundreds digit plus 2 times the tens digit minus the units ...
- 418
10
votes
2
answers
232
views
The special machine
There is a machine, which when you put a number card which has written $x$ on it, it will output a number card with $$x^2+10x+20$$ on it. John has a number card on his hand, then repeated the ...
- 5,560
14
votes
1
answer
695
views
The numbers on blackboard
The numbers $2020,2019,2018,...,1$ are written on the blackboard from left to right.
John repeats the following process until there is only one number left:
John chooses the first two numbers from ...
- 5,560
27
votes
5
answers
2k
views
Google cannot find me
Google cannot find me,
reflected I'm lemon and lime,
googling 'me' is when you fall,
me and meme will answer all.
What am I?
Line 1 hint: Posted I still
Line 2 hint: Take my reflection
...
- 70.4k
4
votes
1
answer
265
views
The motorcyclist's challenge
Three passengers $1,2,3$ starts out moving at constant speeds from $A$ to $B$. At the same time, a motorcyclist $M$ starts out from $B$ towards $A$ to pick the passengers up. As illustrated below:
...
- 6,354
4
votes
2
answers
414
views
The Genius Bank Robber
StackVille Bank & Trust - Robbed!
The Robbery
The bank is being robbed. There are millions in cash in the vault. The lone robber takes the manager to the safe and demands he opens it.
The manager ...
- 2,135
6
votes
2
answers
188
views
The Balls of Death
You have nightmares about a pool ball with the number 1 on it, and an empty box. Why?
Immortality
Imagine, if you will, we are 5000 years into the future. Medicine has evolved and we now are immortal -...
- 2,135
2
votes
3
answers
522
views
The Missing House Number
The Visit
One day I was visiting my sister in Boston and heard a bunch of kids yelling and playing in the yard ( yahd ).
I couldn't see the kids, and hadn't seen my sis for years so I asked her, "...
- 2,135
1
vote
1
answer
328
views
A riddle from the higher mathematics of categories
I've recently been studying some topics in higher mathematics (hint), and it inspired me to create this riddle that I hope some of you enjoy.
What's a structure-imposing map from humans to anything ...
- 2,296
-1
votes
1
answer
133
views
The Team Roster Mystery
Game Day
When the managers of the Tampa Times and St. Pete Sun met for their annual company baseball game, everyone decided by unanimous vote that they wanted a different method of choosing which team ...
- 2,135
1
vote
1
answer
147
views
The Thrilling Chase
Our story takes place in the future. Earth has been invaded by an evil alien species, known by the humans as simply, "The Bots". They are essentially robots, but sophisticated and evil. ...
- 2,135
3
votes
2
answers
392
views
The Marble Game
Johnny vs. Vinny
As brothers, these two are competitive in every aspect of life. Just check out some of my other puzzles, and you'll see my brothers in action.
Today is a classic Marble Battle! The ...
- 2,135
11
votes
2
answers
2k
views
Two Cannons - A Beginner's Physics Puzzle
Standoff
Let's say we have two cannons aimed directly at one another ( as my horrible attempt shown in the image ).
The Angles
The cannon on top is aiming down towards the one on bottom right, and ...
- 2,135
5
votes
1
answer
150
views
Triangular conundrum
Place any three numbers on the vertices of a triangle:
5
/ \
/ \
/ \
8-------4
Calculate their differences, going one way:
5
/ \
-3 / ...
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5
votes
1
answer
18k
views
Programmatically solving a math puzzle with four unknowns and four equations
I have this puzzle and I want to solve by code. I wrote simple code trying to brute force but it fail in one condition
https://dotnetfiddle.net/cJyu3w
How can I solve such problems?
- 53
1
vote
0
answers
606
views
Decode this message to stop the destruction of Science!
An extremist religious organization called "The Redeemed Against Scientific Usurpation of God's Authority", or RASUGA, have converted the world's leading time travel researcher to their ...
- 2,758
8
votes
2
answers
966
views
Big number puzzle
I saw this on rec.puzzles many years ago, but can't find the reference to credit the source.
I am thinking of a large number. If you want to multiply it by a two digit number $ab$ with $a \lt b$, ...
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6
votes
1
answer
209
views
Algebra related puzzle
I have got a puzzle as a Christmas present from a friend of mine and I have managed to solve it while skipping this part, but I would still be interested in how this represents the information that I ...
- 191
-4
votes
10
answers
1k
views
SafeCracker #3 - We've Been Blocked [closed]
Our Last Safe To Conquer
Ok, team, this one might give us a little trouble. Nothing we can't handle though... let's go...
This safe model is "The NevaCrak 9000" - the most secure safe there ...
- 2,135
2
votes
1
answer
120
views
2
votes
2
answers
406
views
Can the sum, difference and product of 2 numbers be perfect squares? [closed]
If we take 2 numbers $x$ and $y$ such that $x>y>0$ and , can $x + y$, $x - y$ and $xy$ all be perfect squares?
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3
votes
2
answers
137
views
Can you have the harmonic, geometric, arithmetic and quadratic mean of 2 numbers all being integers? [closed]
I created this problem looking at the hm-gm-am-qm inequality (hm = $\frac{2xy}{x + y}$, gm = $\sqrt{xy}$, am = $\frac{x + y}{2}$, qm = $\sqrt{\frac{x^2 + y^2}{2}}$ and hm $\le$ gm $\le$ am $\le$ qm).
...
- 91
14
votes
1
answer
349
views
A small team doing their job
Find the unique solution to
$$ 5\,ninja + retook + quarter + turn = \_\,\_\,\_\,\_ + \_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_ $$
where each unknown is a different
_ _ _&#...
- 1,072
8
votes
2
answers
386
views
Houses and Telephone #s
There are 16 houses consecutively numbered 1-16. All houses have 7-digit telephone numbers, numbered consecutively, in the same order. For example, if house #3's phone number is 1111111, house #4 will ...
- 337
4
votes
1
answer
586
views
Analyzing Single-Elimination Tournaments
I know there are many questions/answers about single elimination tournaments out there, but I wanted to approach this question in a more holistic way.
For a single-elimination tournament with N ...
- 337
4
votes
2
answers
288
views
Trickier hand tiling
This should be a little trickier.
Using $20$ rectangles of aspect ratio $1:2$, make two squares.
Use sizes 2,3,7,12,16 in both squares.
And split this list among ...
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1
vote
1
answer
197
views
Make 100€ out of 1€
With the following trick you can turn 1€ into 100€:
$$
\begin{align}
1 \, €
&= 2 \, € \cdot 0.5 \, € \\
&= 200 \, \text{ct} \cdot 50 \, \text{ct} \\
&= 10 \, 000 \, \text{ct} = 100 \, €
\...
- 5,686
7
votes
2
answers
972
views
Videogame salesmen
Two gamers sell their collection of XBOX games. They've got as many Euros as there were games in the collection originally for each game.
They split the money by having the first gamer take 10 Euros ...
user39732
3
votes
2
answers
844
views
Inductive or Deductive Reasoning [closed]
Russell wanted to impress his coworkers. At a meeting, he announces that he can predict anyone's birthday if they tell him their birthday number. To get this famous birthday number, he asked everyone ...
- 47
4
votes
3
answers
951
views
What numbers fill the blanks in 3*3 grid? [closed]
I have a puzzle that I did not know how it could be solved
Which numbers should be filled on the blank spaces ?
I only figure out that 4 + 20 = 24 and 1 + 20 = 21 then 8 + 20 = 28
I am not sure
...
- 41
1
vote
2
answers
535
views
Calculating column number based on Excel alpha column reference [closed]
Here's a super fun brain teaser!!!
Can you give me a mathematical equation to calculate the column number of a Microsoft Excel column, given the alphabetic column reference? Let X, Y, & Z ...
- 23
3
votes
3
answers
427
views
Determine the cost of the book [closed]
Two sisters, Saraha and Jane, go to a book store to buy an algebra book. Saraha is 10 dollars short for the book, and Jane is 1 dollar short. However, if the sisters combine their money, they still ...
- 147
7
votes
1
answer
491
views
Where does the math club meet?
A puzzle from John Conway and Pizza Hut. (The competition has ended, so I think it's okay to post the puzzle here.)
Our school’s puzzle-club meets in one of the schoolrooms every Friday after ...
- 2,206
5
votes
2
answers
345
views
Iterative Floors and Ceilings
$\left\lfloor\dfrac{2016}{\left\lfloor\dfrac{2016}{k}\right\rfloor}\right\rfloor=k\quad;\qquad \left\lceil\dfrac{2016}{\left\lceil\dfrac{2016}{k}\right\rceil}\right\rceil=k$
An integer $k$ with $1\le ...
- 1,948
5
votes
1
answer
196
views
What is the ratio between small and big x-gons?
I have been checking Gamow's question and noticed something! If we draw all diagonals there is a little polygon in the middle of the original polygon if it is odd-gon (odd-gon is defined as the number ...
- 30.2k
11
votes
1
answer
509
views
The adventitious 18-gon
Today I have drawn a regular $18$-gon on a piece of paper. My drawing shows the $18$ vertices of the polygon labeled as $P_1,P_2,\ldots,P_{18}$ in clockwise order, and it also shows all $135$ ...
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