Questions tagged [algebra]
A mathematical puzzle about the manipulation and solution of equations. Use with [mathematics]
66
questions
7
votes
2
answers
831
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
241
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
190
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 ...
- 1,919
6
votes
2
answers
740
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 ...
- 3,646
2
votes
1
answer
308
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.
...
- 9,366
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 ...
- 890
2
votes
3
answers
352
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 ...
- 6,229
-5
votes
1
answer
176
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 ...
- 6,229
12
votes
4
answers
795
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 ...
- 6,229
3
votes
2
answers
216
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
222
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 ...
- 1,943
1
vote
2
answers
159
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 ...
- 6,229
9
votes
1
answer
451
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
633
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