Questions tagged [algebra]

A mathematical puzzle about the manipulation and solution of equations.

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5
votes
2answers
165 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. ...
17
votes
5answers
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 ...
2
votes
3answers
336 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
votes
1answer
146 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 ...
1
vote
0answers
206 views

Number of connections to towers [closed]

We are given longitude and latitude of locations from where the channels are going to be broadcasted, along with the height of tower from which these channels are broadcasted. Also we have been given ...
11
votes
4answers
732 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 ...
3
votes
2answers
195 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
2answers
135 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 ...
1
vote
2answers
134 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 ...
8
votes
1answer
374 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. ...
7
votes
1answer
430 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 ...
10
votes
2answers
216 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 ...
14
votes
1answer
622 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 ...
28
votes
5answers
1k 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 ...
4
votes
1answer
223 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: ...
4
votes
2answers
321 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 ...
6
votes
2answers
164 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 -...
1
vote
2answers
345 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, "...
1
vote
1answer
225 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 ...
-1
votes
1answer
119 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 ...
1
vote
1answer
121 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. ...
3
votes
2answers
345 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 ...
11
votes
2answers
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 ...
5
votes
1answer
136 views

Triangular conundrum

Place any three numbers on the vertices of a triangle: 5 / \ / \ / \ 8-------4 Calculate their differences, going one way: 5 / \ -3 / ...
5
votes
1answer
10k views

How to programmatically solve math puzzle

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 Anyone know of a link or source how to solve ...
1
vote
0answers
591 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 ...
7
votes
2answers
949 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 $a \lt b$, ...
6
votes
1answer
190 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 ...
-4
votes
10answers
963 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
votes
1answer
114 views

The NANNP Grid ( Not another Next Number Puzzle )

Simply figure out the last row...
2
votes
2answers
389 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?
3
votes
2answers
99 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). ...
14
votes
1answer
325 views

A small team doing their job

Find the unique solution to $$ 5\,ninja + retook + quarter + turn = \_\,\_\,\_\,\_ + \_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_ $$ where each unknown is a different _ _ _&#...
8
votes
2answers
378 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 ...
4
votes
1answer
522 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 ...
4
votes
2answers
273 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 ...
1
vote
1answer
187 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 \, € \...
7
votes
2answers
950 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 ...
3
votes
2answers
809 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 ...
4
votes
3answers
859 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 ...
1
vote
2answers
512 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 ...
3
votes
3answers
426 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 ...
7
votes
1answer
444 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 ...
5
votes
2answers
264 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 ...
5
votes
1answer
186 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 ...
11
votes
1answer
406 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 $135$ ...
11
votes
3answers
347 views

Blackboard problem with polynomial

At the beginning the blackboard contains $n$ real numbers, one of which is $0$. In every step, we may take any polynomial such that all its coefficients are currently on the blackboard, we compute all ...
10
votes
2answers
902 views

An ugly formula [closed]

Our teacher wrote the following ugly algebraic formula on the blackboard $$(n+\sqrt{n^2-1})^{4/3}+(n+\sqrt{n^2-1})^{-4/3}$$ Our teacher told us that for some positive integers $n$ this ugly formula ...
14
votes
5answers
2k views

A man bought several liters of wine

Diophantus of Alexandria was a Greek mathematician who lived in the third century (AD). Diophantus wrote a series of books called "Arithmetica", most of which are lost. Among many other ...
20
votes
3answers
1k views

Which is larger? $\sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2}$ versus $5$

Which side is larger? $$ \sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2} \stackrel{?}{\lessgtr} 5 $$ Without using a calculator, computer, or estimating square roots, please determine which side has the ...