# Questions tagged [algebra]

A mathematical puzzle centered around the manipulation and solution of equations.

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### 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 $a \lt b$, ...
177 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 ...
936 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 is. ...
90 views

### The NANNP Grid ( Not another Next Number Puzzle )

Simply figure out the last row...
369 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?
90 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). ...
314 views

### A small team doing their job

Find the unique solution to $$5\,ninja + retook + quarter + turn = \_\,\_\,\_\,\_ + \_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_$$ where each unknown is a different _ _ _&#...
374 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 ...
453 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 ...
263 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 ...
179 views

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 \, € \... 2answers 947 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 ... 2answers 798 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 ... 3answers 643 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 ... 2answers 471 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 ... 3answers 425 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 ... 1answer 428 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 ... 2answers 254 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 ... 1answer 173 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 391 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 334 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 815 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}$$Our teacher told us that for some positive integers n this ugly formula ... 5answers 2k views ### A man bought several liters of wine Diophantus of Alexandria was a Greek mathematician who lived in the third century (AD). Diophantus wrote a series of books called "Arithmetica", most of which are lost. Among many other problems, the ... 3answers 1k views ### Which is larger? \sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2} versus 5 Which side is larger?$$ \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 ...
480 views

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 ...
247 views

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 ...
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"...
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 ...
441 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?...
870 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 ...
631 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 ...
225 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. ...
879 views

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 ...
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### 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 ...