# Questions tagged [formation-of-numbers]

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

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### The result is 7 game

The goal of this game is to find the lowest score for the 10 equations below. 0 ? 0 ? 0 ?...
422 views

### Construct $\sqrt{3}$ using every natural number

Construct $\sqrt{3}$ using every natural number $n\in \mathbb{N}$ (1, 2, 3, 4...) exactly once and the operations addition ($+$) and division ($\div$).
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### A Number Game puzzle

Our team has created 9 math puzzles with ranging difficulty. Let me share one of them. At the beginning a number is given to you. Your objective is to get a different number by making choices. Here's ...
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### How to make 18 from 1, 3, 4, 8

This question was on my sister's 5th-grade homework, practicing order of operations. It was to make 18, using the numbers 1, 3, 4, 8 and the operations +, -, and *. The instructions imply using each ...
231 views

### For what x can we solve $1,2,3,x=5$

This is a variation on the formation of numbers theme. Given $1, 2, 3, x$ in order, and the operations plus, minus, times, divide, and brackets, what single digits can x NOT be? i.e. find a ...
172 views

### Use only 1 2 6 7 to write expressions that equal 31 32 33 34

Construct expressions that equal $31$, $32$, $33$, and $34$ using the numbers $1$, $2$, $6$, and $7$. In each expression, each number must be used exactly once. You addition ($+$), subtraction ($-$), ...
552 views

### 1 0 1 0 1 0 1 0 1 0 1

Start with the digits:       $1\ 0\ 1\ 0\ 1\ 0\ 1\ 0\ 1\ 0\ 1$ You may then add (only!) these simple arithmetic operators:       $+\ -\ \times\ \div$ You may also ...
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### Using only 1s, make 29 with the minimum number of digits

Use the minimum number of ones to make 29. Here is the list of operations permitted: "Standard" operations, such as: $x+y$, $x-y$, $x\times y$, $x\div y$ Negation: $-x$ Exponentiation of two numbers:...
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### 100 using only 5 number of digits

This is a problem from Martin Gardner. For each digit $1\leq d\leq 9$, make 100 using exactly five number of $i$s. Any operation is allowed, brackets as well. For $i=1,2$ I have a solution: 100=...
276 views

### Using 20, 17, 16, 8, 7 to make 9

You can use $+, -, \times,$ or $/$ (namely $\div$). Use all five numbers (20, 17, 16, 8, and 7) only once to make $9$. From what I've been told there are $4$ answers. The only one I've been able ...
145 views

### Some Really Confusing Math

I was talking to a co-worker this morning and he stated that he was able to make both of these statements true using only $1, 3, 5,$ or $7$. He then proceeded to tell me: $1 = 5$ $2 = 4 + 7$ $3 = 1$ ...
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### Google's 20th Anniversary: Make 20 using 6 0 0 6 1 3

Belated 20th Happy Birthday to Google (600613)! Challenge: Use 6, 0, 0, 6, 1, 3 to make the number 20. Rules: Use all numbers, in that exact order. Allowed operations: +, -, x, /, sqrt, (); no ...
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### Fill in the boxes to get the right equation

Here is a math puzzle I had a little bit of hard time with No computers please There is a solution without inverting 6 to 9
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### Use the digits 1, 9, 9, 8 to get 81 [closed]

Using the digits $1, 9, 9$ and $8$ in that order, and the operations $+$, $-$ and/or $\times$ in any order between pairs of digits, create an expression that equals $81$.  Normal precedence rules ...
239 views

### Make all the ones

Given all the digits $0,\dots,9$ and using each digit exactly once, What is the smallest possible number you can make whose digits are all $1$'s? The only operations that are allowed are: ...
194 views

### 1984 - take the digits 1,9, 8 and 4 and make 369

Part II... 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 ...
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### 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 ...
146 views

### A Math Puzzle with a Pattern

Inspired from a puzzle marathon, here is a math puzzle. There is a pattern with this set of numbers (not in the creation though). According to the pattern, what is the logical replacement for the ...
297 views

### Form the biggest squaring number

You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below: Take the square any number you want in the number (you ...
756 views

### make this sum using only +

A bit of a speed question this, first correct answer gets the check. Although you are allowed to use computers, it might be quicker not to. By placing only $+$ signs between some of the numbers on the ...
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### Make 4 4 4 4 = 30,31

Follow up question to Make 5 5 5 5 = 19 Can you find a way to make: $4\ 4 \ 4 \ 4 = 30$ and $4\ 4 \ 4 \ 4 = 31$ by adding any operations or symbols on the left side of the equations? You can ...
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### Maximize the number of factorials in your solution to 6 5 4 3 = 1

Using the same rules as Make 6 5 4 3 = 1, but maximize the number of factorials. You may not take the factorial of 1 or 2. This is harder than it looks. A great answer has six factorials, an ...
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### 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 ...
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### Make 6 5 4 3 = 1

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

### Making 49 from 5, 1, 3, 4 [closed]

I have these numbers: 5, 1, 3, 4. There are four different ways to make 49 - what are they?