# Questions tagged [formation-of-numbers]

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

56 questions
6answers
71k views

### Make numbers 1 - 30 using the digits 2, 0, 1, 8

It's 2018 so let's repeat last year's challenge with new digits. This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all four digits exactly once Allowed ...
6answers
3k views

### Use 2 0 1 and 8 to make 67

Use $2$ $0$ $1$ and $8$ to make the number $67$ RULES You must use all 4 digits. Only the digits 2, 0, 1, and 8 can be used. You can make multi-digit numbers out of the numbers. Examples: 20, 82, ...
2answers
2k views

### Make numbers 93 using the digits 2, 0, 1, 8

I have a 1 to 100 building challenge with 2, 0, 1, 8, all made but 93 is not made. I need your help! This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 8. Rules: Use all ...
2answers
11k views

### Write twenty-four from four numbers

Write 24 using the four numbers 1, 3, 4, 6 and basic arithmetic. Explanations: The given are numbers, not digits, so you can't group them using decimal notation. For example, you can't create the ...
10answers
137k views

### 1 2 3 4 5 6 7 8 9 = 100

The sequence of numbers $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9$ has the property that you can insert mathematical operators in between the numbers from $1$ to $9$ and make the expression evaluate to 100. For ...
10answers
14k views

### Make 5 5 5 5 = 19 [closed]

Can you find a way to make: $5\ 5 \ 5 \ 5 = 19$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
3answers
471 views

### Hiker's Cabin Mystery | Pt. II

See Part I | See Part III Nice one, @GarethMcCaughan! Finally, you've gotten into his computer using the password you managed to decode from his clues... but there's another issue! There is a ...
1answer
169 views

### 1984 - take the digits 1,9, 8 and 4 and make 246

Next year is the 70th anniversary of the publication of the book 1984 by George Orwell. Here is a puzzle to start the anniversary celebrations off a bit early ... Warm up Can you assemble a formula ...
12answers
259k views

### 1 2 3 4 5 6 7 8 9 = 1

This question inspired me to write the same puzzle but instead replace the "= 100" with "= 1" with similar requirements and restrictions. What is the expression with the fewest number of operators ...
16answers
10k views

### A truly amazing way of making the number 2016

Find a mathematical expression that yields the value $2016$ while obeying the following rules: Each of the digits $1,2,3,4,5,6,7,8,9$ is used exactly once Decimal points are allowed You ...
3answers
1k views

### If 6 was 9, or 100 was 64, or M was N

Now if a 6,          Turned out to be 9,          I don’&...
2answers
957 views

### Self-intro to mo-Roman numerals

Here come mo -Roman numerals — just like Roman numerals, only mo’ so.   (Explained as we go.)   What number can spell itself in two different ways ...
1answer
1k views

### New Mathematics forever

This has been (renamed and) refocused on boboquack’s unforeseen solution, which deserves its own puzzle. Right when you thought the good old days of New Mathematics were safely dusted, ...
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, ...
10answers
881 views

### SafeCracker #3 - We've Been Blocked [closed]

Our Last Safe To Conquer Ok, team, this one might give us a little trouble. Nothing we can't handle though... let's go... This safe model is "The NevaCrak 9000" - the most secure safe there is. ...
4answers
2k views

### A truly amazing way of making every possible positive integer

This is a follow-up to "A truly amazing way of making the number 2016": For every positive integer $n$, find a mathematical expression that yields the value $n$ while obeying the following rules:...
1answer
232 views

### The Autonumerigram Challenge [duplicate]

Some phrases both refer to a number, n, and are comprised of n alphabetic characters. I call any such phrase an autonumerigram. For example, four has 4 letters seven plus seven has 14 letters ...
4answers
557 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 ...
2answers
297 views

### Coppers - Make 24 [closed]

The make-24 puzzle is an oldie, but a very fun one at that. Given four different numbers, produce—through a sequence of operations upon only those four numbers—the number twenty-four. For example, ...
4answers
30k views

### Create all numbers from 0-100 only using all of 1,2,3,4 and 5

Create all numbers from 0-100 only using 1,2,3,4 and 5. No repeats and you have to use each number. Also, you can use any operation. I've only gotten to 50 by pure brute force. I think that this might ...
6answers
22k views

### The 10,958 Problem

Here is the task: Write down 10958 using all 1-9 digits in ascending order and only one time. You are allowed to: 1) group digits into numbers 2) use 5 basic operations: + - * / ^ ("^" ...
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: ...
5answers
2k 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 ...
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 ...
16answers
9k views

### Number 88 from the digits 2, 0, 1 and 7?

Can you use the digits 2, 0, 1 and 7 each only once to create the number 88?
7answers
47k views

### Make numbers 1 - 32 using the digits 2, 0, 1, 7

This is similar to the "Four fours" puzzle, but using the digits 2, 0, 1 and 7. Rules: Use all four digits exactly once Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root ...
2answers
602 views

### Ode to convergence

Taking a numeral core (digits: a non-quad four) digits I ordered, then lesser I minused, till evolve I couldn't more. What is this unfathomably clunky poem all about?
11answers
10k views

### Make 6 5 4 3 = 81

Can you find a way to make: 6 5 4 3 = 81 by concatenation and/or adding any of (and only) these mathematical operators: + - × ! ÷ ^ standard parentheses () You cannot add other numbers to the ...
1answer
145 views

### Another loop of integers with consecutive terms adding to a square

The integers 1 to 50 are placed around a circle in such a way that the sum of any two of them which are adjacent is a perfect square. Of these integers, all but the prime integers were removed. ...
4answers
3k views

1answer
854 views

### IBM Research Puzzle – 5-ops implementation of erasure code

I found this interesting puzzle on IBM Research Puzzling Page called Ponder This; specifically, here. Design a storage system that encodes 24 information bits on 8 disks of 4 bits each, such that: ...
8answers
518 views

### Make $1,\dots,15$ using $3, 9, 9, 9$

This was inspired by many puzzles that use three/four numbers to create other numbers. I chose these numbers in particular because of this post. Can you find a way to make all the natural numbers ...
18answers
5k views

### Use the numbers 1-9 to equal 1150 [closed]

Not sure if this is too hard, but it's a more or less simple math puzzle. Use the numbers $1,2,3,4,5,6,7,8,9$ to get an answer of 1150. You can use the operators $+,-,*,/,\hat{}$ You can use ...
3answers
6k views

### Make numbers 1-100 with only four 8s

Make numbers 1, 2, 3, 4, 5,.....100 using only four 8s. You can use multiplication, division, addition, and subtraction. No negatives. You may use exponents. Example: $1 = 8 \times 8 \div 8 \div 8$
3answers
184 views

### Get 20160 with 5 2's and any Mathematical Operator [closed]

Here is a mathematical riddle: Find a way to get 20160 with 5 2's and any mathematical operators you want. Have fun! Don't forget that I said any. Feel free to look online for crazy whacky math ...
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 ...
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 ...
5answers
4k views

### Use two 2's, two 1's and two 8's to make the number 2018

This is another number formation question. You must use each of $2$, $1$ and $8$ exactly twice to make the number $2018$. The rules are Allowed symbols: $+$, $-$, $\times$, $\div$, $($, $)$, \$\sqrt{\...
2answers
459 views

### Make 439204 from Φ (Golden Ratio)

In my last formation-of-numbers question I somehow tricked myself, because I wanted to make a puzzle about a number that looks like a year. But the complicated solution I thought of turned out to be ...