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Questions tagged [formation-of-numbers]

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

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8 votes
1 answer
1k views

Making 1353 using Four fours

As the title says, the goal for this puzzle is making 1353 out of simply 4, 4, 4 and 4. Concatenation is not allowed. Here are all of the allowed operators. Addition (+), Subtraction and negatives (-)...
Alejandro Garcia's user avatar
-4 votes
3 answers
154 views

Use 1 6 7 8 (all numbers) to equal 2 [closed]

Create an equation using 1, 6, 7 and 8 to equal 2. Can use brackets, plus, minus, subtract, multiply.
Number Bond's user avatar
5 votes
1 answer
142 views

Number relations in a number table

I found this puzzle in a school study group. Choices are 9, 10,11, 12, 13. $$ \begin{array}{|c|c|c|c|} \hline 22& 22 & 23 & 24 \\ \hline 22 & 32& 41& 52\\ \hline 23 & 41 &...
Gablin32's user avatar
-2 votes
2 answers
213 views

How do you make numbers 1 - 100 using the digits "2 0 2 4"? [closed]

I'm trying to complete this "2024 Challenge", but I'm still missing quite a lot of numbers. I need your help to finish this challenge. All answers are appreciated. Rules: Use all 4 digits ...
PiMemoryLegend's user avatar
1 vote
0 answers
175 views

Can you obtain a given set of numbers by halving a chosen number? [closed]

Given a set of numbers, I want to check if it is possible to produce the full set of numbers by repeatedly splitting one single starting number into its halves and doing the same for each of the ...
Kevin's user avatar
  • 39
6 votes
4 answers
411 views

Approximate ln(2) out of small numbers

Given numbers 1,2,...n, the goal of this puzzle is to make a number as close to the mathematical constant $\ln(2) ≈ 0.69314718055$ as possible. Rules You can only use the four mathematical ...
CrSb0001's user avatar
  • 2,413
-2 votes
1 answer
109 views

How to make all the numbers ranging from 1-30 only using the numbers 1, 5, 0, 4 [closed]

You can use the numbers 1, 5, 0, and 4 but you can't square and cube, you can't use any other numbers, you can't use the numbers more than once, your answer can't be rounded, and you MUST use all the ...
SALAHTHEGOAT's user avatar
0 votes
1 answer
161 views

Getting The Numbers 33 Through 99 Only Using 2, 0, 2, and 4 [closed]

How do you get the numbers 33-99 by using the numbers 2,0,2,4
user88484's user avatar
4 votes
4 answers
429 views

How to make 2012 by using 2, 0, 1, 2?

How to make $2012$ by using $2, 0, 1, 2$? Allowed Operations: Addition, Subtraction, Multiplication, Division, $!$ (factorial), subfactorial ( $!n$), primorial (product of the first $n$ primes), ...
Thirdy Yabata's user avatar
6 votes
4 answers
756 views

How to get the numbers from 50 - 100 with the numbers 2, 0, 2, 4

All I need is 56-59, 69, 73, 75- 77, 79, 86, 90-94, 99. I've done the rest but I would love to hear other solutions. Rules: Use any of the following operations: basic operations (+ - x /), to the ...
bob's user avatar
  • 79
-2 votes
1 answer
141 views

Make numbers 1 - 30 using the digits 2, 0, 2, 5

Try to make all numbers 1-30 using the digits 2, 0, 2, 5. Rules: Use all four digits exactly once. Allowed operations: $+,−,×,÷,! \text{ (factorial)}, !! \text{ (double factorial)}, !!! \text{ (...
WOWOW's user avatar
  • 421
0 votes
1 answer
93 views

Insert operators into 3 5 7 = 7 [closed]

How can you insert any math symbol/operation () ! - + x / square root etc into 3 5 7 = 7 without adding any numbers or changing the order? For example, 3-7+5=1 or 3+7-5=5. Also, try to solve 3 7 5 = 2,...
CSS's user avatar
  • 27
18 votes
4 answers
5k views

Make 27 using 1, 1, 1, 1

Make the number 27 using 4 instances of the digit 1. You must use all 4 digits to make it count. Here are the allowed operators: Addition (+), subtraction (-), multiplication (*), division (/) Square ...
Alejandro Garcia's user avatar
4 votes
2 answers
501 views

Make expressions equal to 6 using exactly four 4s

You must use all four 4s. You may use addition (+). You may use subtraction (-). You may use multiplication, such as with asterisks (*) and/or grouping symbols. You may not use any division. You ...
Olive Stemforn's user avatar
3 votes
1 answer
266 views

Constructing 2024 from the first 7 natural numbers

Can you use each number 1, 2, 3, 4, 5, 6, 7 exactly once, the four operations +, -, *, / and the parentheses to construct the number 2024? Bonus: can you find multiple distinct solutions? No computers ...
Dmitry Kamenetsky's user avatar
3 votes
2 answers
366 views

Approximate e out of small numbers

Given the numbers 1, 2, ..., n the puzzle is to try to make a number as close as possible to the mathematical constant $e$ using only the four mathematical operations +, -, *, / and parentheses (...
Simd's user avatar
  • 7,845
12 votes
6 answers
10k views

Make numbers 1 - 30 using the digits 2, 0, 2, 4

Try to make all numbers 1-30 using the digits 2, 0, 2, 4. Rules: Use all four digits exactly once. Allowed operations: $+, -, \times, ÷, !$ (factorial), x^y (exponentiation), √ (square root). ...
jac's user avatar
  • 137
8 votes
1 answer
911 views

Escape Room Puzzle: numbers in Christmas trees

I was sent this puzzle by a friend who's recently attended an escape room, but it's really not coming to me. I wondered if anyone had seen similar puzzles and could suggest an answer?
EB3112's user avatar
  • 183
6 votes
1 answer
355 views

Add as few plus signs as possible to make equation true

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
Will.Octagon.Gibson's user avatar
18 votes
11 answers
5k views

How to solve 1 2 3 4 5 = 5 4 3 2 1 (insert five pluses to make it equal)? A thorough solution needed

I consider it an amazing though very challenging puzzle: 1 2 3 4 5 = 5 4 3 2 1 One must insert exactly five pluses (i.e. five addition signs) somewhere between those ten displayed figures in such way ...
Alexander's user avatar
  • 595
-2 votes
1 answer
318 views

Create numbers from 1-100 using 1846

Create all numbers $1$ to $100$ using equations made up of $1,4,6,8$. Rules: Use all four digits exactly once Allowed operations: $+,\,-,\,\times,\,\div,\,!$ (factorial), exponentiation ($a^b$), ...
sonia ahuja's user avatar
10 votes
4 answers
2k views

A Prime Number equation using all nine digits once

Create an equation with the following conditions All numbers must be one or two digit prime numbers You can only use + and - and = No other math operators You must use all the nine (single) digits (...
RogerA's user avatar
  • 6,627
-4 votes
1 answer
242 views

Using 8 6 4 2, how do you get to 30

8 6 4 2 =30 in that order using only + - X
Karen Chappell's user avatar
4 votes
13 answers
4k views

Let's make a huge number with only tiny numbers

Using only three 1s and two 2s (i.e. 1,1,1,2,2), can you generate the number 55? You can use all mathematical operators you know, such as floor function, factorial, powers/indices*, etc., but ...
user86497's user avatar
2 votes
1 answer
142 views

If 123x45 = 1, 22+222=0, 8979:4=5, 56319=2 what is 781-32=?

If 123x45 = 1, 22+222=0, 8979:4=5, 56319=2 what could be the solution to 781-32=? Found it on an maths board and became desperate over time.
Guestos's user avatar
  • 29
5 votes
1 answer
233 views

Number encoding puzzle

An "ancient" writing system for numbers was discovered: How would the number 75 be represented with this code? (Two symbols) I think I made it too hard, here are some hints:
anton-tchekov's user avatar
3 votes
2 answers
213 views

How can this equation make sense?

Think a bit creatively and tell me why is this equation correct
RogerA's user avatar
  • 6,627
-2 votes
1 answer
281 views

Creating a high number from this grid using minimal mathematical operations

I'm creating a puzzle (pictured below). From this grid, how could I output a 10-digit number? The tiles cannot be moved or changed. Instruction-wise, I would like to provide my players with some ...
Will's user avatar
  • 595
-2 votes
4 answers
288 views

Sixteen Two's to get Two Thousand and Twenty-Two

Get the number 2022 by only using the number 2 a maximum of 16 times. There is a solution. Allowed: $+$ $-$ $*$ "$()$" "$\frac x y$" $x^y$ Note: When you use $2^2$, it counts as ...
WOWOW's user avatar
  • 421
2 votes
1 answer
397 views

How is the tree colored?

Not relevant fiction context Paul's journey in the mathematical forest began this early morning. You know, he is a Biomathologist! He saw a lot of spectacular plants, geometrical flowers and fractal ...
10010100102ohno's user avatar
26 votes
7 answers
2k views

Approximate pi out of small numbers

Given the numbers 1, 2, ..., n the puzzle is to try to make a number as close as possible to pi using only the four mathematical operations +, -, *, / and parentheses (brackets). You don't have to use ...
Simd's user avatar
  • 7,845
25 votes
3 answers
6k views

Combine 1,3,3,7 to get 10

I tried lots of combinations but could not find a solution. Each number has to be used exactly once, the allowed mathematical operators are Addition: + Subtraction: - Negation: (unary prefix) - ...
Karl Karlsen's user avatar
-2 votes
1 answer
153 views

2023 From Numbers 1-15

Using the numbers 1, 2, 3,..., 15, in that order, how can you make the number 2023 using the +, -, $\times$, and $\div$ operations. (You can use as many parentheses as you want.)
Ronchen Luo's user avatar
8 votes
1 answer
900 views

2023 Squared From Squares

Without moving or removing any number, replace each of the triangles by either $+$, $-$, $\div$ or $\times$, and insert as many sets of parentheses as you want, in order to make the following equality ...
Ronchen Luo's user avatar
3 votes
0 answers
164 views

encode in encode

Today, a cryptic message was received by Area 51: Bananatexteismarvellous605185682252125223459314283216133301 2 The staff managed to figure out that some 2 digit ...
BETABOT's user avatar
  • 31
-6 votes
1 answer
682 views

How to make 93 using only 2 0 2 4

How to make 93 using only 2 0 2 4? The digits can be used only once. You can use $+,-,*,/,Sqrt,X^y,!,!!,nCr,nPr$ You can also group 2 and 2 to make ‘22’ and you can also use the above method to make ...
Erniewong's user avatar
1 vote
1 answer
172 views

Continue the row of numbers: 1, 3, 9, 13, 65, ...?

Yesterday, I stumbled across a series of numbers that I could not solve. Maybe one of you can figure it out? 1, 3, 9, 13, 65, …?
HeterPawker's user avatar
2 votes
0 answers
185 views

Do puzzles like "write 120 using four 8" have a specific name?

Here on puzzling SE there is the category "calculation puzzle", but it's very broad. I'd like to know if somebody gave a specific name for such puzzles.
mau's user avatar
  • 2,095
12 votes
5 answers
3k views

2023 From Single Digits

Using only the digits, 1, 2, 3, 4, 5, 6, 7, 8, and 9, in that order, how can you make the number 2023 using the +, -, ✕ and ÷ operations? (You can use as many parentheses as you want)
RonnieChen's user avatar
6 votes
2 answers
1k views

499 and the Gamma Function

Folks elsewhere in this very same site have been working hard to express positive integers in the binary system using merely four ones and four zeros. They have been allowed to use the four basic ...
Bernardo Recamán Santos's user avatar
12 votes
8 answers
3k views

Four ones and four zeros

Which is the smallest natural number that can not be expressed in base 2 with precisely four ones and four zeros using the four basic arithmetic operations, exponentiation, concatenation, brackets, ...
Bernardo Recamán Santos's user avatar
13 votes
1 answer
721 views

Find the lower 8-digits number such that

This one come from newspapers in France, where this week is the "mathematics week", and some problems are proposed to kids. This single one is easy and funny: Find the lowest 8-digit number, ...
franck vivien's user avatar
12 votes
4 answers
3k views

Create number 985 using 1 3 5 7 9

Use $1, 3, 5, 7, 9$ in any order to make number $985$: You must use all $5$ digits $1, 3, 5, 7, 9$ exactly once. You can make multi-digit numbers out of the numbers, e.g. $13$ or $975$. $+, -, *, /, ...
ThomasL's user avatar
  • 12.2k
8 votes
1 answer
1k views

Make expressions equal to 1,000 using exactly six 1s

You may use up to two subtraction symbols (no negation symbols). You may use up to two decimal points. You will use one vinculum for division (no "/"). You may use concatenation of digits ...
Olive Stemforn's user avatar
1 vote
2 answers
287 views

Smallest number to be made in one way

Take the numbers 1,3,4,6,9,10. We can make other numbers using these numbers and the operations +,-,*,/. E.g. we can make 244 with: ...
Simd's user avatar
  • 7,845
3 votes
1 answer
259 views

Two many restrictions

Using only the number 2 several times, form the numbers 2, 22 and 222. The following operations are available: addition subtraction multiplication division exponentiation Each of these operations ...
Manish Kundu's user avatar
  • 2,684
6 votes
1 answer
388 views

Forming 2023 with 7s

Idea from Ed Pegg Jr. Can you form 2023 using only the digits 7, exponentiation, modulus and factorial operations?
Dmitry Kamenetsky's user avatar
5 votes
4 answers
2k views

Largest number using 1, 2, 3, 4 [closed]

Find the largest number using digits 1,2,3,4. Allowed operations are addition, subtraction, multiplication, division, exponents, brackets and decimal point. No other digits besides one of each of 1, 2,...
ThomasL's user avatar
  • 12.2k
12 votes
2 answers
3k views

Create 76 out of 1,2,3,4

You can use +,-,*,/,^,! and sqrt operations (no concatenation) and all numbers must be used once and only once. for example, 75 can be made by $3×(4!+2-1)$ and $81=(2-1)×3^4$ I've been trying to reach ...
Ri Ignis's user avatar
  • 123
-4 votes
1 answer
243 views

What is the biggest number you can make with 6 9s?

What is the biggest number you can make with 6 9s? These are the allowed operators: Subtraction Addition Multiplication Division Factorial Exponents Square root Floor and Ceiling functions Arbitrary ...
one23456789's user avatar

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