Questions tagged [formation-of-numbers]

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

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4
votes
2answers
445 views

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 ...
6
votes
2answers
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 ...
24
votes
4answers
11k views

The largest integer made of 1,2,3,4

What is the largest integer $A$ that can be produced from the four digits $1,2,3,4$ subject to the following rules? Each of the digits $1,2,3,4$ is used exactly once. Juxtaposition of digits is ...
-2
votes
1answer
166 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 ($-$), ...
3
votes
2answers
526 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 ...
29
votes
10answers
9k views

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:...
11
votes
2answers
3k views

How should I approach using two 8s and two 3s to make the number 24?

Use two $8$s, two $3$s, and basic arithmetic operators ($ +, -, \times , \div$, parentheses) to make the number $24$. (You may not join numbers together to form new numbers, like $ 8, 3\...
4
votes
1answer
148 views

An unambiguous number puzzle

One is four, two is six Three is one, four is one Five is nine, six is five Seven is nine, eight is nine Nine is two, ten is five Eleven is seven, twelve is eight. What is thirteen? Note: the ...
12
votes
8answers
3k views

Create all numbers from 1-100 using 1,3,3,6

Create all the numbers from $1$ to $100$ using the numbers $1$,$3$,$3$, and $6$. You can only use each number once, except for the $3$, of which you have two. You can use addition ($x+y$), ...
1
vote
5answers
272 views

Create all numbers from 1-100 by using 1,3,3,7

Create all the numbers from $1$ to $100$ using the numbers $1,$$3,$$3,$ and $7.$ You can only use each number once, except for the $3,$ of which you have two. You can use addition $(x+y),$ ...
43
votes
10answers
30k views

Can you make 1 1 1 1 = 5? [closed]

Can you find a way to make 1 1 1 1 = 5 by adding any operations or symbols? You can use symbols such as these: +, -, *, !, ^, (). It is not limited to this list. Good Luck! P.S. You can not add any ...
5
votes
6answers
297 views

2019 to every day of the month

The grumpy professor looked at his class and said - ok so now it is 2019 can you use the four digits individually with *, +, -, /, ^ (raise to the power of) and ! to make each day of the month? You ...
11
votes
4answers
5k views

Create the numbers 1 - 30 using the digits 2, 0, 1, 9 in this particular order!

Inspired by the last year's "2018 four 4s challenge", I thought it's time to welcome 2019 by a similar challenge. This time you have to use the digits 2, 0, 1, 9 in this particular order to create the ...
0
votes
4answers
19k views

10 9 8 7 6 5 4 3 2 1 = 2018

Add the four basic operators × ÷ + −: 10 9 8 7 6 5 4 3 2 1 to get the total 2018. Keep the order; do not combine numbers. Don't use any brackets. Use all four operators at least once.
3
votes
1answer
131 views

Triskadecimal Emojis

[This puzzle is heavily based on one from video game Zero Time Dilemma.] I have one of those weird individualist friends--to give you an idea, he spells his name H-E-N-🔟-R-Y. ...The 🔟 is silent, y'...
12
votes
4answers
4k views

Doubling/tripling puzzle: make 1 from 1536 in as few steps as possible

You start with the number 1536. Your mission is to get to 1 in as few steps as possible. At each step, you may either multiply or divide the number you have, by either 2 or 3; but, only if the result ...
9
votes
2answers
1k views

Ten-digit number that satisfy divisibilty rules for 2,3,4,5,6,7,8,9,10&11

Question: Arrange the digits 1,2,3,4,5,6,7,8,9,0 to make a ten-digit Number that satisfies all of the divisibility rules for 2,3,4,5,6,8,9,10,&11. BONUS: make the number also divisible by 7
23
votes
6answers
77k 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 ...
19
votes
5answers
753 views

A riddle that has been killing me the whole day

So I'm walking around in London and found the following number riddle. The rules say, that what ever pattern you find, must be true for the rows as well as the columns. The answer in level 1 is for ...
2
votes
15answers
3k views

Just One Line! Really? [closed]

Add ONLY ONE line (does not have to be a straight horizontal line or in other words, doesn't need to be an axis aligned to the equal sign) to make the equation below true : EQUATION : $...
10
votes
17answers
6k views

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=...
22
votes
9answers
6k views

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 ...
5
votes
2answers
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 ...
13
votes
9answers
2k views

Use 0, 5, 7 and 1 to make 89

Assemble a formula using the numbers $5$, $0$, $1$, and $7$ in any order to make 89. You may use the operations $x + y$, $x - y$, $x \times y$, $x \div y$, $x!$, $\sqrt{x}$, $\sqrt[\leftroot{-2}\...
2
votes
1answer
144 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: $1 = 5$ $2 = 4 + 7$ $3 = 1$ ...
7
votes
6answers
3k views

Use 6, 5 and 3 to make 57

Assemble a formula using the numbers $5$, $6$, and $3$ in any order to make $57$. You may use the operations $x + y$, $x - y$, $x \times y$, $x \div y$, $x!$, $\sqrt{x}$, $\sqrt[\leftroot{-2}\uproot{2}...
11
votes
7answers
1k views

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
4
votes
3answers
1k views

1984 - take the digits 1,9, 8 and 4 and make 123 - Part III

Part III ... 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 ... I think this is the ...
1
vote
4answers
381 views

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 ...
4
votes
1answer
206 views

Palindromic number puzzle - make 505 from 20202

Can you assemble a formula using the numbers $2$, $0$, $2$, $0$, and $2$ in any order so that the results equals $505$. You may use the operations $x + y$, $x - y$, $x \times y$, $x \div y$, $x!$, $\...
5
votes
2answers
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: ...
1
vote
3answers
190 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 ...
1
vote
1answer
197 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 ...
4
votes
1answer
140 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 ...
9
votes
1answer
296 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 ...
6
votes
8answers
548 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 ...
4
votes
9answers
1k views

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 ...
3
votes
2answers
755 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 ...
14
votes
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, ...
4
votes
2answers
888 views

Use 2, 0, 1 and 8 to make 71

Use all and only the digits $2,0,1,8$ once each to make the number $71$. Allowed operations; anything not on this list is banned: $+,-,\times,\div, ()$ (parentheses and/or choose function) ...
7
votes
3answers
220 views

Is this number unique?

Inspired by Interview Question or Pathbreaking puzzle and A121808. Start with $1$, and count the number of times $1$ occurs, and report this in the format 'number of ones:1', i.e. the next term is $...
15
votes
7answers
4k views

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 ...
4
votes
6answers
4k views

Writing numbers puzzle

How do you write 23 using only the number 2? 34 using only the number 3? 56 using only the number 5? 100 using only the number 9? You can use only the numbers said, but any math you want in order ...
10
votes
6answers
2k views

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 ...
11
votes
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 ...
22
votes
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 ...
-5
votes
1answer
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?
1
vote
1answer
64 views

Find the operators

Assume you are using a basic calculator and press these numbers in order. Replace each question mark with plus, minus, multiply and divide may be used, but no sign should be used more than once. In ...
6
votes
1answer
91 views

The Yerata number system

There are only a few words for numbers in the Yerata1 language. Here are all of them, in random order: imu tere nuopo rowintom rowintom rowintom imu tere nuopo re nuopo rowintom re nuopo nuobo imu ...
-6
votes
2answers
3k views

Make numbers 33-100 using only digits 2,0,1,8

Use the numbers 2, 0, 1, and 8 (ALL of them...only ONE time each) to make every integer from 33 to 100. Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root and Parentheses No ...