Questions tagged [algebra]

A mathematical puzzle about the manipulation and solution of equations.

Filter by
Sorted by
Tagged with
10
votes
2answers
204 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
594 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 ...
27
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
220 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
303 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
157 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
331 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
222 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
105 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
115 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
329 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
133 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
7k 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
587 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
947 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
186 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
954 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
110 views

The NANNP Grid ( Not another Next Number Puzzle )

Simply figure out the last row...
2
votes
2answers
382 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
93 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
324 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
377 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
497 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 ...
0
votes
1answer
184 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
805 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
832 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
506 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
441 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
262 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
403 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
345 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
880 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 ...
19
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 ...
7
votes
3answers
489 views

Six fruit baskets

There are six fruit baskets with apples, bananas and plums on the table. The number of bananas in each basket is equal to the total number of apples in the other five baskets together. The number of ...
8
votes
2answers
251 views

Cheherazad, the carpet salesman

Cheherazad, the carpet salesman, has bought a rectangular piece of carpet. Unfortunately, Cheherazad's has lost his tape measure and he has no other measuring instruments. However, he finds that if he ...
12
votes
5answers
3k views

Turning wine into water

Niccolò Tartaglia was an Italian mathematician, engineer and bookkeeper, living in the 16th century in the Republic of Venice. Tartaglia published many books, including his "General Trattato di Numeri"...
12
votes
2answers
2k views

The grazing cows of Sir Isaac Newton

Sir Isaac Newton's book "Arithmetica Universalis" contains the following famous puzzle: In $4$ weeks, $12$ cows graze bare $3\frac13$ acres of pasture land, and in $9$ weeks, $21$ cows graze ...
5
votes
4answers
457 views

And the average is 51.5625

Freddy removes four consecutive even numbers from the set $\{1,2,3,\ldots,n\}$. Freddy then computes $51.5625$ as the average of the remaining $n-4$ numbers. Which four even numbers did Freddy remove?...
22
votes
2answers
883 views

The year 2016 is approaching

Do there exist integers $r,s,t\ge100$ such that the decimal representation of $(r+\sqrt{s})^t$ is of the form $~~~\ldots\ldots2015\,.\,2016\ldots\ldots$? (In other words: the four digits before the ...
2
votes
4answers
632 views

Fifteen white rhinoceroses

Fifteen white rhinoceroses are standing in a line. Each of them weighs an integer number of pounds. For each rhinoceros (except the leftmost one), its weight plus twice the weight of its left neighbor ...
2
votes
1answer
228 views

Dancing, dancing, dancing

My friend Kim told me: Last week I went to an afternoon party. I was the last guest to arrive. I looked around and counted (not including myself) altogether 14 grown-ups and 17 children. ...
11
votes
2answers
885 views

Vladimir and his motorbike

Vladimir wants to take his two daughters to their Dacha (weekend house) which is located 66 kilometers away from their home. Vladimir's motorbike has a maximum speed of 50 kilometers per hour; with ...
8
votes
2answers
473 views

Bumblebees and Honey bees

The current market price of 175 honey bees is more than the price of 125 bumblebees, but less than the price of 126 bumblebees. Is it possible to buy 3 honey bees and 1 bumblebee for altogether at ...
5
votes
3answers
974 views

Witches and Cats

This being Halloween, we will consider the problem of witches and their cats. The whole crowd is out tonight, naturally, and an interested observer, seeing them fly by (yes, witches' cats fly), ...