# Questions tagged [algebra]

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

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### 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
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 ...
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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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 ...
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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
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. ...
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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
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 ...
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172 views

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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 ...
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
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
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
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
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 ...
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