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Questions tagged [formation-of-numbers]

For puzzles about forming numbers using other numbers and mathematical operations.

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-4
votes
1answer
858 views

Using the digits 2, 3, 4 make an expression for 30

Write an expression using exactly one 2, exactly one 3, and exactly one 4 to make 30. For each problem, you must use all three of these: Division Factorials (just for regular factorial use, no ...
0
votes
3answers
256 views

Fill in the parentheses [closed]

$()+()+()+()+()=30$ How can you fill in the parentheses with the numbers $1, 3, 5, 7, 9, 11, 13$ to make the above equation true? Repeats are allowed, but you must fill in all of the parentheses! ...
2
votes
2answers
367 views

90s Number Puzzle

So here's how it works: Take the digits from 1991. You can use the digits in any order, only once (you can't make a 19 or 91), with any operation sign to get answers between 1-100. For example: $4=(1+...
12
votes
3answers
758 views

Replace each ? in the expression with a digit or operator

In the following expression, replace each ? with either a digit or an operator: 8?5+??5-9?+3 so that it can evaluate to: <...
7
votes
5answers
1k views

Simple but interesting math puzzle [duplicate]

Four numbers are available: $1$, $3$, $4$ and $6$. Every number must be used once and only once with (some of) the operations $+$, $-$, $\times$, $\div$ to form the number $24$. It's from the book "...
0
votes
11answers
2k views

Make the number 17 using only 2, 3, and 4 [closed]

Is it possible to make the number 17 using only 2, 3, and 4? Using the numbers only once and any operation, including factorials and other more advanced math. And it would have to be exactly 17.
-1
votes
2answers
163 views

Form n/2 with n amount of ANY number

For every $n, m \in \mathbb{N}; n,m > 1$, construct a method to produce $\lfloor\frac{n}{2}\rfloor$ using n ms. You can use: $$x+y$$ $$x-y$$ $$x*y$$ $$\frac{x}{y}$$ $$x^y$$ $$x\bmod y$$ $$\sqrt[k]{...
12
votes
3answers
652 views

Who will find the number on their own hat first?

Both $A$ and $B$ have numbered hats on their heads. $A$ and $B$ both cannot see his/her own hat, but they can see other one's hat. $A$ sees number on $B$'s hat as $5$ and $B$ sees $A$'s number as $4$. ...
7
votes
5answers
7k views

Alternating numbers

Alternating numbers are numbers in which all digits alternate between even and odd. For example: 2703 and 7230 are alternating ...
2
votes
1answer
152 views

decipher this modified sum operation,

This is crossposted from Math.SE, the original question is here $1+2+3+4 = 61$ $2+3+4+5 = 52$ $3+4+5+6 = 51$ $4+5+6+7 = 50$ $7+8+9+10 = ?$
29
votes
13answers
14k views

10 9 8 7 6 5 4 3 2 1 = 2016

Add the four basic operators $\times\div+\,\;-$ and optionally brackets to: $10 \quad 9 \quad 8 \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1$ To get the total $2016$. Rules: We are ...
-7
votes
5answers
304 views

Largest number with two hands [closed]

Pretty short one, really. Given your two hands, what's the largest number you can represent? Some example representations: 1 finger on each hand: that's 2. 2 fingers on one hand, and 3 on the other: ...
2
votes
1answer
204 views

Depressed Numbers [duplicate]

$12 = 0$ $1234 = 1$ $123456 = 2$ $12345678 = 4$ $369 = 2$ $248 = 3$ $2 = 0$ $3 = 0$ $5 = 0$ $7 = 0$ $11 = 0$ $13 = 0$ What does: $123456789 = ?$ Why? Hopefully isn't too hard, please ask if you ...
3
votes
0answers
303 views

How is it possible to make 8 (…) 8 (…) 8 = 6? [duplicate]

$$8\text{ }8\text{ }8 = 6$$ Add in any required number of mathematical symbols to make the above equation work. How is this possible? Can somebody explain?
18
votes
3answers
2k views

Puzzling 101: Sums of seventeen numbers

After reading a bit in Meta and the help section, I'm still not sure whether this qualifies as a "good" puzzle in the spirit of the site, but the votes will show - I liked it when I encountered it, ...
4
votes
2answers
198 views

Autonumerograms

An autonumerogram, or self-enumerating number, is a number that can be read as describing itself by providing a pairwise inventory of its own digits. For example, 22 (two 2's) and 14233221 (one 4, two ...
5
votes
3answers
3k views

Express the number $2015$ using only the digit $2$ twice

Can you use only two instances of the digit $2$, along with the mathematical operations below, to create an expression that evaluates to $2015$? Allowed operations: arithmetic operations: addition ($...
8
votes
1answer
2k views

A basic calculator, a simple game. What was I playing at? [duplicate]

Yesterday I was doodling around with my very simple calculator as shown in the picture. First I would enter a few digits to make an integer (i.e. no decimal places). Then I would perform a simple ...
14
votes
4answers
480 views

A Perfectly Primitive Parameter Permuter

A simple challenge for the mathematically inclined. Find a function $f\left( {{x_1},{x_2},{x_3},{x_4}} \right)$ such that $$\begin{gathered} f\left( {2,3,4,5} \right) = 1 \hfill \\ f\left( {1,3,4,...
6
votes
3answers
2k views

What numbers fill the blanks to satisfy the equation?

Complete the grid shown below with the digits 1 to 6 to make the sum correct. Perform each mathematical operation in the order shown, from left to right, e.g. 1 + 2 x 3 is treated as (1 + 2) x 3 = 9. ...
7
votes
4answers
2k views

A Threes Of Cake

This question is similar to my other question Twos For Thought, which arguably was a better pun but I decided to recreate the question, except with threes! How many threes do you need to get to the ...
-4
votes
2answers
212 views

Using numbers form a number

Using 7,8,9 and basic mathematical operations form the number 327600. Use every digit exactly once. Note: Allowed Operations: $+,-,/,*, {}^{\displaystyle\large\hat{}} ,!,\sqrt{}$
4
votes
4answers
565 views

Twos For Thought

How many twos do you need to get to the number $100$ exactly? Example: $22+22+22+22+2^2+2^2+2^2$ This example method uses 14 twos and is obviously not ideal. Can you find a way that uses the least ...
8
votes
3answers
1k views

$\pi$ Day puzzle one to twenty

Create the numbers from 1 to 20 Using $\pi$ Normal arithmetic operation $+ - * /$ Square root $\surd$ Exponential $(X^Y)$ Negative() minus sign $-$ Floor() function, express between $[ x ]$ $[ ...
34
votes
4answers
3k views

Display a number using a scientific calculator with most keys are stuck

Your have a scientific calculator such that most of the keys are unable to be pressed. The only keys that work are those for the functions $$ x^2 \;\; \sqrt{x} \;\; x!\;\; \exp\;\; \ln\;...
13
votes
5answers
3k views

What is the smallest positive integer, which can not be written without repetitions of digits and using arithmetics only?

Suppose you are allowed to use all 10 digits (0,1,2,...9) at most once each; 4 arithmetic operations ($-$,$+$,$\times$,$\div$), each any number of times; parenthesises to group operations; and you can ...
2
votes
3answers
252 views

Number formation with digits given

How do you form the number 1000 with the digits, 1,2,3 and 4? The mathematical operations that can be are addition, subtraction, multiplication, division, parentheses, percentages and factorials. ...
4
votes
5answers
1k views

The game of Sevens

There is a popular game, named Four fours, where you have to find the shortest mathematical expression for every number from $1$ to $n$, using only the number $4$ and some operators. My variant of ...
8
votes
2answers
1k views

$\tau$ is greatest! $\tau$ is all (from 1 to 20)

(This is basically an extension of $\pi$ Day puzzle one to twenty) $\tau$ is greater than $\pi$ and $\tau>\pi$. Create the numbers from $1$ to $20$ using only: Tau ($\tau$, equivalent to $2\pi$) ...
5
votes
3answers
5k views

Create integers from 1 to 50 using only one integer and other functions

Your task is to create all the integers from 1 to 50 (inclusive) using only a single integer $x$ and... Addition ($+$), Subtraction($-$), Multiplication($\times$), and Division($\div$) Floor($\left \...