# Questions tagged [algebra]

A mathematical puzzle about the manipulation and solution of equations.

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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
$\left\lfloor\dfrac{2016}{\left\lfloor\dfrac{2016}{k}\right\rfloor}\right\rfloor=k\quad;\qquad \left\lceil\dfrac{2016}{\left\lceil\dfrac{2016}{k}\right\rceil}\right\rceil=k$ An integer $k$ with $1\le ... 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 ... 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$135$... 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 ... 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 ... 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 ... 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 ...