# Questions tagged [arithmetic]

For puzzles involving addition, subtraction, multiplication, or division.

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160 views

### My Sister's Six Children

My sister has six children whose ages add up to 40. The ages of any two of her three boys have a common divisor greater than 1, and so do the ages of any two of the ages of her three girls. However, ...
746 views

### A Tour Around a Triangle

Place the 18 even integers between 2 and 36 in the empty nodes of this triangular graph in such a way that if a path is drawn by coloring in red all the edges joining any two nodes whose numbers add ...
2k views

### My Three Children

The sum of the ages of my three children is 40. Though the ages of my two daughters are relatively prime (i. e. they have no common divisor), the age of each of them does have a common divisor greater ...
495 views

### A partition of 1000 into nine parts

The sum of nine whole numbers is 1000. If those numbers are placed on the vertices of this graph, two of them will be joined by an edge if and only if they have a common divisor greater than 1 (i.e. ...
1k views

### Four Marathon Runners

Four marathon runners, each identified with a positive whole number, sit around a table. Each of them notices that their own number has a common divisor with the number of the runner sitting on his ...
14k views

### Make numbers 1-30 using 2, 0, 1, 9

This is very similar to the 2, 0, 1, 8 problem. Just try to make all numbers 1-30 using the digits 2, 0, 1, 9. Rules: Use all four digits exactly once Allowed operations: +, -, x, ÷, ! (factorial), ...
114 views

### Calculate cost of excess water consumed [closed]

100 Liters of water is available equally in a month for consumption among 5 members @ 1 dollar per liter. If some members don't use their own available 20 liters, it can be used by the others at the ...
2k views

### A partition of 100 into nine parts

The sum of $9$ positive natural numbers, not necessarily distinct, is $100$. If placed appropriately on the vertices of the following graph, two of them will be joined by an edge if and only if they ...
404 views

### The mathematical quiz

There are 4 equations. What should I put in place of the ? in the last one? 1 + 4 = 5 5 + 3 = 11 7 * 7 = 61 10 - 1 = ?
588 views

### Curiosity of February 5$^{th}$

Some people write February 5$^{th}$ using the md format, as $2.5$ or alternatively as $2/5$. Note that $2.5 \times \frac25 = 1$. Is there any other date satisfying $a.b \times \frac{a}{b} = 1$? ...
352 views

### Six sisters on the ski lift

The sum of the ages of six sisters known to me is 92. Though there is no single whole number greater than 1 that simultaneously divides the ages of any three of them, I did notice this morning, while ...
605 views

### My forgotten PIN

I´ve forgotten my PIN, a four-digit number. All I remember is that it is a perfect square, and that it has at least one digit in common with every other four-digit square number. What is it?
4k views

### My five daughters

The sum of the ages of my five daughters is 43. The ages of any two of them have a common factor greater than 1. How old are my daughters?
826 views

### A unique partition of 200 into 6 parts

The sum of six positive integers is 200. If placed appropriately on the vertices of this graph, two of them will be joined by an edge if, and only if, they are not relatively prime, that is, if they ...
200 views

### Continue sequence

Son asked such a task. Continue the number sequence 5, 7, 8, 12, 11.... The son is in the second grade. They studied the operations of addition, subtraction and ...
460 views

### How many multiplications to find n^k given n, for general k?

I was looking at the nice puzzle Find $n^{23}$ with the least multiplication. My first instinct for this would have been to find $n^{2^i}$ for each $i$ first and then multiply these together as ...
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 ...
514 views

### Why you shouldn't buy cheap puzzle books

Backstory contains important information, but nothing hidden. Also, tl;dr parts are bolded, but I can't guarantee I didn't forget bolding some part. Recently there's been a grid-deduction craze here ...
171 views

### Turn based Number game

You and a friend take turns saying positive integers greater than one. You can't say a number that is a multiple of previous numbers or a sum of multiples of previous numbers. For example, if A says 3 ...
159 views

### Complete the equality (medium-hard)

Complete the equality to make it true: 1 1 1 1 1 = 945 Using similar logic, solve for this: 1 1 1 1 1 = 80 Info: You should ...
277 views

### Complete the equality

Complete the equality to make it true: 1 1 1 1 = 5 You can add any math operation or symbol to the left side. You cannot change right side nor the ...
135 views

### Remove two digit/symbol to find equality

Find the equality by removing any two digits or symbols (of course, except equal sign) $4\div3+63=9-23\times7\div3$ For example, if the equation below was given, Example: $91-81=45+12\div3-85$ ...
920 views

### Buttons on an old non-scientific calculator are less sensitive

All 5 numbers are entered in an ascending order. These numbers are in an arithmetic progression. The value of the fifth number, i.e. the largest number, is less than 99. While adding these ...
23k views

### The 10,958 Problem

Here is the task: Write down 10958 using all 1-9 digits in ascending order and only one time. You are allowed to: 1) group digits into numbers 2) use 5 basic operations: + - * / ^ ("^" ...
3k views

### Yet another matchstick puzzle

Inspired by this post, here there is my attempt at a matches' puzzle. The expression 1 = 850 - 9 - 6 is obviously wrong: move exactly three matches to obtain a correct expression. Rules are: This ...
343 views

### Little Red Solving Hood goes one-stop swapping

Moral of the story:   Two stored values may be swapped arithmetically with 4 or fewer variable references. Puzzle of the story:   Can you exemplify the moral?   (With 10 or ...
418 views

### Sum self enumerated digits

Please fill in the entire summations for lines 4 through 9 and just the total for line 1,000,000.         1.     1   =   1   ...
2k views

### Two Three-Digit Numbers Added to Make Four-Digit Sum. No Number Can Repeat Itself.

A friend posed this question to me a few days ago, and I just haven't been able to get it off of my mind. "There are ten numbers from 0 to 9. You can use any number you like in the box, but the ...
551 views

### The Vacuumed Quotes

A colleague of mine likes to put his favorite quotes up on the fridge using those little magnetic letters. This morning the cleaner came and accidentally vacuumed up all the letters. We were able to ...
338 views

### Series Problem By Gpuzzles - I Have Doubt [duplicate]

gpuzzles.com is one of my favorite sites along with StackExchange, but can someone please elaborate on the answer? Problem: Can you solve the number series problem by replacing boxes with numbers 1, ...
235 views

### The Autonumerigram Challenge [duplicate]

Some phrases both refer to a number, n, and are comprised of n alphabetic characters. I call any such phrase an autonumerigram. For example, four has 4 letters seven plus seven has 14 letters ...
289 views

### KenKen Zen: The Cluelessening

As our KenKen voyage of cluelessening­* began, some clues remained entirely hidden from us.  Though much remains to be discovered, we may now be entrusted with all clue amounts at once.&...
527 views

### KenKen Zen: A journey begins

Let us shy away from the materialistic opulence of 361- cell KenKen layouts (−9 to +9, squared).  Let us contemplate a modest KenKen journey, unburdened by gratuitously ...
2k views

### Sum other numbers

Begin with a flagrantly erroneous summation and a woefully vacant substitution table. 234 + 5 Digit 2 3 4 5 6 7 8 ------- ...
763 views

### Honeydripping around the clock

What path could a honeybee follow, beginning and ending at top center, visiting every empty cell exactly once and dripping 2 drops of honey into the last cell? Start ...
301 views

### How to fill a honeymoon

How can a honeybee visit all cells exactly once in this crescent shaped honeycomb, beginning at the bottom tip and ending at the top? The starting cell, at ...
279 views

### H-one-one-oneycomb

What path could a honeybee follow to fill all cells with honey, beginning and ending at the center and visiting every cell exactly once? At first the only ...
375 views

### Get the largest number using the crazy circuit board

There is a crazy circuit board with three kinds of elements which can change the signal value. All intersecting paths are connected (but paths touching by a single point are disconnected). There is ...
179 views

### Arithmetic Puzzle

The British Independent and i newspapers run what they call an "Arithmetic Puzzle", which comprises a grid of nine cells, with each cell separated from the others by arithmetic symbols: (+ - / *), and ...
592 views

### A (Simple) Arithmetic puzzle

I'm hoping this one was not posted here already, tried to search a bit and didn't find it. It's a really nice brain teaser: Add arithmetic operators (plus, minus, times, divide) to make the ...
2k views

### A moderate visual number puzzle

In the following diagram, each red dot represents a positive number. The dot-numbers on each of the five circles spell out either a word (each dot corresponding to a letter) or a number (each dot ...
329 views

### It is related to a type of mathematics game

Start with two digits from $1\dots9$ to form a $2$-digit number. Multiply this number by a single digit from $1\dots9$. Add the result to another two digit number from $1\dots9$, and calculate the ...
1k views

### Difficult sequence

Here I go : $3 + 5 + 6 = 15 \ 18 \ 72$ $5+ 5 + 6 = 25 \ 30 \ 94$ $5 + 6 + 7 = 30 \ 35 \ 85$ $5 + 5 + 3 = 25 \ 15 \ 73$ $9 + 4 + 7 = 36 \ 63 \ ?$ Replace ? with appropriate number
969 views

### How old was Matthew when his brother died?

When Sam's father died, Sam's uncle, Matthew (his fathers only brother) was twice the age of Sam minus 14 years. As Sam and Matthew grew older they became friends. When the younger of the two turned ...
156 views

### Age of Samantha and her grandchildren

Samantha is suffering from Alzheimer's and uses math to help remember things. Samantha has two grandchildren. Samantha youngest grandchild's age when raised to the power of the square root of her ...
214 views

### In which year(s) could I have been born, if you know my unexact age in an unexactly dated source (unexact means exact up untill years) [closed]

At some point in 2015 I filled out a form and wrote 41 for my age. What are my possible birth years? Some trivial clarification about the information above: The age 41 is only exact up until the ...
734 views

### What's My Number (Math Riddle) [closed]

I am thinking of a number. I multiplied by 3, subtracted by 8, doubled the result, and added 14. Then i added on 50% of what I had and subtracted 11. Then i divided by 5. After all that, I was left ...
433 views

### The oldest wins the prize, but they won't tell their age

I'm trying to design a problem that should be as close as possible to the following setup, while meeting some requirements about its solutions. Initial setup There is a group of more than 2 people ...