Questions tagged [formation-of-numbers]
For puzzles about forming numbers using other numbers and mathematical operations. Use with [mathematics]
441
questions
-1
votes
2
answers
111
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 ...
1
vote
0
answers
171
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 ...
- 39
4
votes
1
answer
179
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 ...
- 2,241
-2
votes
1
answer
100
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 ...
- 11
-1
votes
1
answer
139
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
- 19
4
votes
4
answers
419
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), ...
6
votes
4
answers
733
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 ...
- 79
-2
votes
1
answer
117
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{ (...
- 422
0
votes
1
answer
90
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,...
- 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 ...
- 191
4
votes
2
answers
458
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 ...
- 1,788
3
votes
1
answer
262
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 ...
3
votes
2
answers
359
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 (...
- 7,845
12
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).
...
- 137
8
votes
1
answer
896
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?
- 183
6
votes
1
answer
348
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!
...
- 9,876
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 ...
- 595
-2
votes
1
answer
313
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 ($a^b$), ...
- 29
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 (...
- 6,049
-4
votes
1
answer
219
views
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 ...
- 99
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.
- 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:
- 153
3
votes
2
answers
213
views
How can this equation make sense?
Think a bit creatively and tell me why is this equation correct
- 6,049
-2
votes
1
answer
278
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 ...
- 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 ...
- 422
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
...
- 851
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 ...
- 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) -
...
- 259
-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.)
- 459
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 ...
- 459
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 ...
- 31
-6
votes
1
answer
648
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 ...
1
vote
1
answer
170
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, …?
- 19
2
votes
0
answers
184
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.
- 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)
- 574
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 ...
- 18.8k
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, ...
- 18.8k
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, ...
- 1,484
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 $975$.
$+, -, *, /, ...
- 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 ...
- 1,788
1
vote
2
answers
286
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:
...
- 7,845
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 ...
- 2,704
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?
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,...
- 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 ...
- 123
-4
votes
1
answer
240
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 ...
- 395
1
vote
5
answers
376
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
...
- 143
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
...
- 395
2
votes
5
answers
517
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, ...
- 395