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Questions tagged [formation-of-numbers]

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

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2
votes
2answers
334 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 ...
3
votes
1answer
515 views

Find the rule : triplet number into Positive Integer

These are triplets of numbers into positive integers: ...
40
votes
16answers
5k views

What is the smallest set of letters that can spell any integer? [closed]

Today my 9-year-old nephew told me that he can spell any integer in English using only 9 letters. This is how he's doing it: ...
5
votes
4answers
1k views

Making 1-50 from 2016

Make the numbers 1-50 using the numbers 2 0 1 6 in the given order. 1.You must use all four digits. 2.You may not use any other numbers. 3.You may use +, -, x, ÷, square root, squaring and cubing, ...
1
vote
2answers
224 views

modified 3x3 panmagic squares

This is a modified 3x3 panmagic squares. The square is divided into 2 triangles. Numbers 1 to 9 is arranged to upper triangles. Numbers 10 to 18 is arranged to lower triangles. All rows, all columns, ...
5
votes
1answer
586 views

Check digit number : Find the maximum number of distinct ways

Find the maximum number of elements in a set containing combinations of three digits (from 0 through 9) with the following rules: Each digit can be used more than once. Any two combinations in the ...
4
votes
2answers
297 views

The mathy square strikes back!

This is a follow-up question to Does this mathy square have any solutions? (And how many?). Consider a 7x7 grid of math operators o and numbers ...
14
votes
4answers
1k views

Does this mathy square have any solutions? (And how many?)

Consider a $5\times5$ grid of math operators and numbers that encodes 8 math equations: A + B = C = + + + + D + E = F + = = = = G = H + I There are 3 horizontal ...
-2
votes
3answers
697 views

Can you express 1844 in a curious way? [closed]

Can you find integer values for $p$ and $q$ with $p,q\in\{0,1,2,\ldots,9\}$ so that the following equation holds? $p^q - q^p = 1844$
5
votes
2answers
519 views

Reveal all five equations

Five men enter a bar. 1st man order 1 Pepsi and 1 Cocacola 2nd man order 2 Pepsi and 1 Cocacola 3rd man order 3 Pepsi and 1 Cocacola 4th man order 4 Pepsi and 1 Cocacola 5th man order 5 Pepsi and ...
4
votes
1answer
2k views

Expressing numbers using 0, 1, 2, 3, and 4

The least number that cannot be written using the numbers 0, 1, 2, and 3, each exactly once, and any combination of standard arithmetic operations (including factorials) is 41. What is the least such ...
4
votes
3answers
322 views

Number wheel Challenge!

Much like the Word-tank-wheel challenge, but numbers! Find a number that can 'rotate' in a way that the origin number and its rotations must be divisible (i.e. whole number) by the number of times it ...
6
votes
4answers
513 views

Find the next number in the sequence [closed]

One tough puzzle to solve : Find the next number in the sequence : 5,105,74,712,37,? Options are : a. 2008 b. 57 c. 507 d. 98 e. 44 What is the next number, and why? Puzzle ...
12
votes
8answers
2k views

Make 1 with any 3 of the same numbers

Is it possible to make 1 with any 3 numbers, all the same, such as using 3, 3 and 3 or 6, 6 and 6? Can you think of a proof which will work no matter which number it is? Trig functions allowed.
13
votes
2answers
609 views

Help me find my friend!

I need your help! My friend has gone missing and I have no clue where he could be! However, he did manage to get a message out to me: Kidnapped. Send help. I am here: port town. $\left\lfloor\...
-5
votes
4answers
443 views

A Wonderfully Tricky way of Making any Positive Integer [closed]

Make all positive integers, starting from $1$, using: Exactly four $4$'s (and no other digit), concatenation being allowed, Any standard mathematical symbol(s) and operation(s) not listed below. ...
-5
votes
3answers
1k views

Make 82 With Numbers and Dots

How do you make 82 with the numbers $4, 5, 6, 7, 8, 9, 0$ and 8 dots. Get creative! You can use any mathematical operation, and the dots can be used in any mathematical way. No ratios. You must ...
-5
votes
2answers
1k views

Make 24 and 30 using the digits 3 and 4

First, write an expression using exactly one 3 and exactly one 4 to make 24. Second, write an expression using exactly one 3 and exactly one 4 to make 30. Math You Can Use for each problem: ...
1
vote
1answer
454 views

Riddle with functions [duplicate]

The following is a riddle, that is not so easy as it seems. Using the numbers 1, 3, 4, 6 only once, you must use any of the functions (addition, multiplication, division, subtraction) in order to form ...
11
votes
2answers
333 views

Make a certain number with an unusual calculator

The Kasio Kool-Kalk™ is a poorly-designed calculator with only two buttons, labelled $[A]$ and $[B]$. Pushing $[A]$ replaces the currently displayed number $x$ with $2-\frac{1}{x}$. Pushing $[B]$ ...
7
votes
2answers
569 views

Please make x and y and z

This puzzle continues "Please make 1 and 2 and 4". A mathematical expression is feasible, if it obeys the following rules: Any real number may be used One may use brackets "(" and ")" to structure ...
0
votes
1answer
1k views

24 game… with exponents!

You may have seen the 24 game where you take four numbers and try to make 24 using the numbers and mathematical operations. However, I present a twist on the 24 game: with an exponent. Here are the ...
14
votes
1answer
2k views

Hello, I am a pretty big number. Add a line to make me many things

I am a pretty big number: Here are a few challenges for you: Add a line to make me a millennium. Add a line to make me a millennium and ten. Add a line to make me a century and one. Add a line to ...
1
vote
4answers
898 views

Use six 6s in an expression that equals 1,000

Given: six 6s Goal: Construct an expression with value $1,000$ Rules: Use all six digits in each expression. No other digits are allowed. Concatenation of digits is allowed. One horizontal ...
-4
votes
1answer
861 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
257 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
391 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
772 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
3k 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
662 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
308 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
307 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
481 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
575 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 ...