**66 arithmetic questions.**

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. ...

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 ...

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 ...

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 ...

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: + - * / ^ ("^" ...

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 ...

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), ...

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 ...

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 ...

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 = ?

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 $a.b \times \frac{a}{b} = 1$?
...

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?

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?

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 ...

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 ...

Son asked such a task. Continue the number sequence5, 7, 8, 12, 11....The son is in the second grade. They studied the operations of addition, subtraction and ...

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 ...

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 ...

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, ...

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

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 ...

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 ...

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 ...

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

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

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: $91-81=45+12\div3-85$
...

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 ...

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 ...

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

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 ...

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 ...

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 ...

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 ...

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
...

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.&...

I have to fill a whole 3x3 grid in such a way that the sum of each row, column, and main diagonal is 69. I couldn't find any logic to fill it up. I have to use distinct numbers from 1 to 60 for this. ...

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

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Ten years before Alice's age is 4 times John's age. Ten years later, Alice's age is 2 times John's age. How old is John?

Just got a simple question from a friend; still thinking. Let's share it! Is it possible to get a, b, c when you have a⊕b, b⊕c, a⊕c ?where ⊕ is the boolean ...

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