Questions tagged [formation-of-numbers]

For puzzles about forming numbers using other numbers and mathematical operations. Use with [mathematics]

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The operator acts on two numbers to give the following outcomes [closed]

The operator • acts on two numbers to give the following outcomes: 20•2=51 9•8=0 7•3=66 23•14=0 25•2=56 30•12=364 16•9=259 15•22=0 What is the value of 20•1? A. 0 B. 19 ...
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4 votes
4 answers
401 views

Create all of the integers from 1 to 100 using 1, 5, 5, and 7

All four numbers must be used for each solution, but they may appear in any order. Permitted: the 4 basic mathematical operations, square root symbol (maximum twice per solution, and the 2 is implied)...
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  • 41
6 votes
2 answers
702 views

Compact mathematical expression [closed]

Make a mathematical expression whose value is equal to 2 that uses all the digits 0, 1, 2, ... 9 exactly once and uses as few other mathematical symbols as possible.
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0 votes
2 answers
218 views

Four 4s to make a 4 [closed]

Shown below is an equation with four 4s on the LHS and a 4 on the RHS with 4 rectangular boxes and 3 ovals. Make this equation correct by replacing the rectangular boxes by 4 separate single items ...
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  • 38.8k
0 votes
4 answers
178 views

Solve for 69 using only 1 9 9 2 in that order [closed]

You must use all the digits of $1 9 9 2$ in that order to come up with $69$ as the answer. For example $ - (1 + \sqrt {9})! + 92 = 68 $ but you must solve for $69$.
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3 votes
2 answers
188 views

Using Prime numbers to get 100 and 1000

Using the digits 1 to 9 exactly once create a set of one or two digit prime numbers. Use those prime numbers and the math operations + - / * and parantheses to get 100. Then use those exact same ...
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  • 38.8k
5 votes
2 answers
244 views

How do you produce the number 5, using only 3 eights?

How do you produce the number 5, using only 3 eights? The 4 operations (+ - x and division) + square root and factorial are allowed but no extra numbers (no squaring).
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10 votes
1 answer
426 views

How do you get the number

How do you use the format 1_*_ _ _ _ _ _ _ _ to get 222,222,222 using only the numbers 1-9 only once
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  • 109
6 votes
4 answers
803 views

Paris and Wife Matchstick

Here are two matches dates that I hold with love in my heart: The current sum is 1970 + 1997 = 3967. You must requisition at most 10 matches so that the sum is "as big as possible". We will ...
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  • 5,557
2 votes
1 answer
135 views

Alien decimal numeral system, part II

(continuation...) My alien friend said "do you think our system is strange? You need to have a look at our neighbour country, this is how they do it...", and then he showed me their ...
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27 votes
1 answer
1k views

Alien decimal numeral system

During our travels around the galaxy we found many alien cultures with different number systems. However, this specific civilization was quite interesting: they had a decimal numeral system, just like ...
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3 votes
1 answer
183 views

Some blissfully ignorant math?

I was playing around with the code for my game the other day in an effort to create some unique effects. One thing I created was what I called an "ignorant assignment" in which I applied ...
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5 votes
4 answers
2k views

Obtain numbers from 0 to 9 with the digits of 2022 in that order

The title says (nearly) all. Write the digits $2$ $0$ $2$ $2$ in that order and apply mathematical operators to obtain all values from 0 to 9. What's allowed: The four basic operators, $+ - * /$ ...
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  • 2,067
4 votes
1 answer
188 views

Fractions and Fractional Numbers

Using fractions and fractional numbers of the digits $1$ to $10$ and only the mathematical operations of addition, subtraction, multiplication, and division, including parenthesis (e.g. $1 + 2 - (3 * ...
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  • 38.8k
6 votes
2 answers
2k views

Math puzzle: I know the answer, what is the equation? Use all digits 1-9

A few years ago, my child brought a puzzle home from their 6th-grade math teacher. The solution was to use all the numbers $1−9$ only once and make the equation true. Using a spreadsheet, I was able ...
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2 votes
1 answer
223 views

What number comes next in this evenly doubled sequence?

I've been playing around with sequences lately and found a pretty evenly doubled sequence of single digit numbers: 1, 12, 30, 64, 65, 156, 175, 368, 369, 371, 752, 753, 1524, 1525, 3060, 3073, 6168, ...
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1 vote
1 answer
161 views

An oddly formed sequence?

I've been playing around with sequences lately and came across one that was rather, odd. $101$, $123$, $147$, $189$, $191$, $213$, $217$, $279$, $...$ Hints Let $N_i = 101$... Can you determine the ...
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0 votes
1 answer
282 views

The maze of everlasting flowers

You were recently caught trespassing on the queen's hunting grounds. The punishment for this crime is a miserable experience the locals call the maze of everlasting flowers: The full resolution of ...
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3 votes
1 answer
465 views

A number like waldo?

What is the smallest whole number that when its individual digits are summed, produces a number 4 digits long? For example, the number $5357$ is no where close since $5 + 3 + 5 + 7 = 20$. Note: I'm ...
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2 votes
1 answer
193 views

Fill each blank with a digit 1-9 without any repetition [closed]

Fill the following place holders with digits in the range from 1 to 9. Each digit only appears once and make the equation sum up to 100. _ /_ * _ + _ * _ * _ / _ + _ * _ = 100 Also, what is the ...
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  • 39
2 votes
2 answers
167 views

How can I create a programmatic solution to a formation of numbers problem?

There is a common formation-of-numbers puzzle in which the solver is supposed to take predetermined collection of numbers, permitted operators, and a desired result; then perform mathematical ...
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3 votes
2 answers
305 views

It's kind-of like Minesweeper

Have you ever played "Minesweeper" or "Lights Out!" and wondered what it would be like to reverse the process? Me too! Say hello to a 10 by 10 grid that I like to call "Number ...
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3 votes
1 answer
197 views

Let's settle our differences

Can you complete this grid and expose the existing relationships? There are no complex operations (e.g. no exponents, square roots, functions, etc), additionally the numbers are all natural numbers ...
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3 votes
2 answers
244 views

Seven 2s with seven math operations

Linked to A four digit number using exact same 4 digits A number with same repeated digits is called a Repdigit or Monodigit number https://en.wikipedia.org/wiki/Repdigit Can you write an equation for ...
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  • 38.8k
-3 votes
1 answer
228 views

Everything needed to solve this cipher is on Puzzling Stack Exchange [closed]

5444 ---> lcxxfy 1906 ---> pstbqjilj 1582 ---> tcxvbpixrpejooat 1431 ---> dohhsfb 888 ---> uvqta 605 ---> noacomputers 618 ---> ylibz 425 ---> ...
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  • 1,215
12 votes
6 answers
4k views

A four digit number using exact same 4 digits

ABCD is a 4 digit number where A,B,C and D are 4 distinctly separate digits between 1 and 9. Using any of the following math operations and the digits A,B,C and D exactly once get the number ABCD. ...
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  • 38.8k
4 votes
4 answers
2k views

Make an equation from expression "1 4 9 100" [closed]

Fill the gaps of the expression $1$ $4$ $9$ $100$ with mathematical operations $+,-,*,/$, physical units and an $=$ sign, such that a correct equation is created. Example: expression $1$ $100$ $...
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  • 11.5k
1 vote
1 answer
1k views

Make 1-100 using 2 0 2 2

You may use the following: Addition [e.g. 2+2] Subtraction [e.g. 2-2] Multiplication [e.g. 2x2] Division [e.g. 2/2] Decimal point [e.g. 2+.2] Exponents [e.g. 22] {tetration is NOT allowed} Square ...
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2 votes
5 answers
403 views

Largest pair of consecutive numbers, not greater than a million, that can be expressed with four fours [closed]

What is the largest pair of consecutive numbers, not greater than a million, each of which can be expressed using precisely four fours and an assortment of standard operators (including concatenation, ...
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-3 votes
6 answers
299 views

Make 93 using 2, 0, 2, 2 and a least powerful set of operations [closed]

Use some mathematical operations to make an expression equal 93. You must use each one of the digits 2, 0, 2, 2 exactly once, and no other digits. To score the solutions, your set of operations used ...
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  • 2,788
4 votes
1 answer
1k views

Find three ways of forming the number 100 using 3,3,5,7

As it says in the title. Rules: anything not explicitly allowed is forbidden. use 3, 3, 5, 7 and multiplication, division, sum, difference, unary minus, and exponentiation in any order. Parentheses ...
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  • 2,961
8 votes
3 answers
692 views

Calculation - the hard way

This is a puzzle I love to play with my math students and I hope you will enjoy it too: You are given the numbers 1, 2, 3, 4, and 5 exactly once. Your target is a number, e.g. 36. Can you create a ...
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  • 285
-4 votes
1 answer
124 views

How to open the lock from this safe?

The puzzle is as follows: The figure from below shows a lock mechanism used to store sensitive data microfilms from a certain lab. This mechanism is magnetic and consists in numbered buttons which ...
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-4 votes
2 answers
97 views

A challenge to make 1 - 100 [closed]

So this challenge is you have (don't have to) make the numbers 1 - 100 by using the numbers 1, 3, 4, 6 only once. I'm stuck on how to make 54. Can anyone help me? P. S. You can use +, -, ÷, x, ! And ...
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10 votes
4 answers
446 views

Not so boring numbers

This is inspired by this and this and more similar ones. Let us consider formation of a given positive integer N by the following rules You may use only one digit, which one is your choice and you ...
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  • 10.1k
9 votes
4 answers
2k views

Make 38 using the least possible digits 8

This is a follow up question to this one, which was: Make the number 1998 using the minimum amount of digits 8. Your allowed operations are +, -, *, /, ^, % (percent). You need not use only integers ...
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  • 28.8k
1 vote
5 answers
2k views

Make numbers 1 - 40 using digits 2, 0, 2, 1

Using only the digits in the year 2021 and basic mathematical operations (+, -, × and ÷), how many of the numbers from 1 to 40 can you make? Not all of the numbers are possible! You may use each digit ...
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-4 votes
5 answers
174 views

A Triad of Pies

Make the 41 integers between -20 and 20 (-20, -19, ..., 0, 1, ...20) using only the four basic arithmetical operations, square root, the floor function, and, Surprise Surprise, exactly 3 π’s. No more ...
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  • 146
3 votes
4 answers
833 views

Make numbers from 1-10 with 5 3s

In this puzzle book, I came across a question that goes like this: Make the numbers from 1-10 using 5 3s. Rules: You are only allowed to use the four basic arithmetic operators ($+, -, \times, \div$...
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  • 869
2 votes
3 answers
106 views

Form a magic square with assorted numbers

Arrange the following numbers in a way such that all rows, columns and the diagonals add up to the same number. ...
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-4 votes
1 answer
133 views

Use only πs to get e

I am taking this puzzle from inspiration from the Four Fours to get Pi puzzle. The puzzle rules are just slightly different. Here are the rules: You are trying to get as close to e as possible with ...
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5 votes
2 answers
140 views

Numbers side by side

Ok, so here's a little puzzle I got. I have five different numbers. They all have different amount of digits. If you place them side by side you see the number 32767 How is this even possible!? ...
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  • 14.5k
7 votes
4 answers
826 views

Sum of digits of sum of digits of sum of digits

The following question was asked in a competitive exam for which I am preparing and I was unable to solve it (in fact I am completely clueless about it). So, I am asking for help here. Given a number ...
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4 votes
1 answer
156 views

Constant puzzle

A constant is hiding behind this puzzle, can you tell which? 4 $\rightarrow$ 2 $\rightarrow$ 1 $\rightarrow$ 1 $\rightarrow$ 1 $\rightarrow$ $\dots$ ? $\rightarrow$ ? $\rightarrow$ ? $\rightarrow$ $\...
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  • 5,557
1 vote
1 answer
95 views

Add operators to make the equation correct, and give 3 ways to do so

I'm trying to solve this puzzle: Add operators to make the following equation correct: 4 4 4 4 = 2. Give 3 ways to do so. You are allowed to use brackets if necessary, but no rearranging of numbers ...
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  • 869
7 votes
1 answer
280 views

This puzzle's value is 334

The 28th of october is valued by 40. This sentence is valued by 17. This paragraph is valued by 143. This puzzle is valued by 334. Can you give the value of Puzzling StackExchange?
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  • 5,557
-3 votes
2 answers
151 views

Using the number 8 6 4 2 = either 19 or 17 [closed]

The numbers can only be used once. You can use any operator from BEDMAS.
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  • 9
-2 votes
2 answers
121 views

Using the numbers 8642 = 9 [closed]

Using any calculation in BEDMAS use the numbers 8645 = 9 Numbers can only be repeated once.
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  • 9
6 votes
0 answers
268 views

Even and primes puzzle?

These are secret numbers that increase regularly. What are the next two numbers? If you like numbers, it will be fun. $2^3 \times224299$ $2^2 \times 3^2 \times 19 \times 3557$ $2 \times 5 \times ...
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  • 61
1 vote
4 answers
430 views

Express numbers 1 - 100 using only 1, 2, 3, 4

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