Questions tagged [formation-of-numbers]

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

Filter by
Sorted by
Tagged with
-2 votes
1 answer
77 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
0 answers
47 views

1 2 challenge to get it using symbols to get it from 1 to 10 [closed]

$1^2=1$ $1\times2=2$ $1+2=3$ $\lfloor (1/.\bar2) \rfloor =4$ or $\lceil\sqrt{12}\rceil$ $1/.2=5$ $(1+2)!=6$ $d/dx(1)+\lfloor e^2 \rfloor=7$ $\lceil 1\pi \rceil+\lceil(!2)\pi\rceil=8$ $\lfloor 1\pi \...
Othniel Fatiregun's user avatar
-3 votes
0 answers
75 views

1 1s challenge to get 1 to 10 with including symbols [closed]

1*1=1 1+1=2 round(square root(11))=3 roundup(square root(11)=4 round(1φ)+round(1π)=5 round(1φ)+roundup(1π)=6 round(1π)+roundup(1π)=7 roundup(1π)+roundup(1π)=8 1/.1~=9 1/.1=10
Othniel Fatiregun's user avatar
4 votes
4 answers
404 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
702 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
-4 votes
1 answer
85 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
  • 177
0 votes
1 answer
89 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
442 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
2 votes
1 answer
252 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
350 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
  • 7,816
11 votes
6 answers
9k 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
  • 119
8 votes
1 answer
890 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
340 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
4k 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
  • 533
-2 votes
1 answer
310 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
  • 6,049
-4 votes
1 answer
198 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
138 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
229 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
  • 6,049
-2 votes
1 answer
276 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
286 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
  • 177
2 votes
1 answer
396 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
25 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
  • 7,816
25 votes
3 answers
5k 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
152 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
603 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
169 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
182 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
  • 2,085
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
719 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
  • 11.9k
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
284 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
  • 7,816
3 votes
1 answer
256 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
  • 2,694
6 votes
1 answer
387 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
  • 11.9k
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
239 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
1 vote
5 answers
375 views

Reviving the Ruins of Number Kingdom

The great wizard Factorial surveyed the empty buildings with an ever-increasing sense of dread. The staff of recursion he held was incredibly powerful and could do great damage in the wrong hands. In ...
DontMindMe's user avatar
22 votes
2 answers
5k views

Make e using 1, 2, 3, 4, 5, 6, 7, 8, 9

Can you make $e$ with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9? You can only use the digits once. The allowed operators are listed beloẉ. Addition Subtraction Multiplication Division Square root ...
one23456789's user avatar
2 votes
5 answers
516 views

Make the numbers 1-100 using 1,7,3,4

I made this puzzle myself. As the title says, you must make the numbers 1 to 100 using the numbers 1,7,3,4 - in that order. All numbers must be used. The allowed operators are below: Addition, ...
one23456789's user avatar
19 votes
2 answers
1k views

What extra number did I form?

My friend and I are each trying to form the integers from $0$ to $100$ using the numbers $2, 3, 8, 9$. We are only allowed to use the five basic operations: addition, subtraction, multiplication, ...
isaacg's user avatar
  • 5,957
10 votes
2 answers
1k views

A square number that is a concatenation of at least 25 squares

A pen and paper challenge: Write down a number whose square (repetition allowed) is the concatenation of at least 25 nonzero squares. examples 7, 13, 12: Their squares are the concatenation of 2 ...
Retudin's user avatar
  • 8,294

1
2 3 4 5
9