Questions tagged [algebra]

A mathematical puzzle about the manipulation and solution of equations. Use with [mathematics]

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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.
gyancey's user avatar
  • 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 ...
Gabe White's user avatar
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 ...
Laska's user avatar
  • 1,666
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 ...
Chengarda's user avatar
  • 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 ...
Rishabh Jain's user avatar
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. ...
Retudin's user avatar
  • 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 ...
nonuser's user avatar
  • 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 ...
Culver Kwan's user avatar
  • 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 ...
Culver Kwan's user avatar
  • 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 ...
Culver Kwan's user avatar
  • 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 ...
Vlad Barkanass's user avatar
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 ...
Display maths's user avatar
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 ...
Culver Kwan's user avatar
  • 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. ...
asg's user avatar
  • 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 ...
asg's user avatar
  • 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 ...
Culver Kwan's user avatar
  • 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 ...
Culver Kwan's user avatar
  • 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 ...
Tom's user avatar
  • 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: ...
Eric's user avatar
  • 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 ...
John S.'s user avatar
  • 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 -...
John S.'s user avatar
  • 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, "...
John S.'s user avatar
  • 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 ...
Galen's user avatar
  • 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 ...
John S.'s user avatar
  • 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. ...
John S.'s user avatar
  • 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 ...
John S.'s user avatar
  • 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 ...
John S.'s user avatar
  • 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 / ...
JMP's user avatar
  • 35.6k
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?
Amjad's user avatar
  • 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 ...
Thomas Markov's user avatar
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 $a \lt b$, ...
Ross Millikan's user avatar
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 ...
Isti115's user avatar
  • 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 ...
John S.'s user avatar
  • 2,135
2 votes
1 answer
120 views

The NANNP Grid ( Not another Next Number Puzzle )

Simply figure out the last row...
John S.'s user avatar
  • 2,135
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?
Magic turtle's user avatar
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). ...
Magic turtle's user avatar
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 _ _ _&#...
Roman Odaisky's user avatar
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 ...
user18842sos's user avatar
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 ...
user18842sos's user avatar
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 ...
theonetruepath's user avatar
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 \, € \...
A. P.'s user avatar
  • 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 ...
user avatar
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 ...
aksh's user avatar
  • 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 ...
RM SH's user avatar
  • 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 ...
DubMart's user avatar
  • 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 ...
asha iraddi's user avatar
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 ...
Colonel Panic's user avatar
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 ...
Roby5's user avatar
  • 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 ...
Oray's user avatar
  • 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 $135$ ...
Gamow's user avatar
  • 45.4k