Questions tagged [formation-of-numbers]

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

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votes
4answers
2k views

Make an equation from expression "1 4 9 100" [closed]

Fill the gaps of the expression $1$ $4$ $9$ $100$ with mathematical operations $+,-,*,/$, physical units and an $=$ sign, such that a correct equation is created. Example: expression $1$ $100$ $...
4
votes
2answers
950 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) ...
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 ...
4
votes
6answers
6k 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 ...
4
votes
3answers
262 views

Use digits 3 3 5 to make 67 or 97

Rules: All 3 digits — $3$, $3$, and $5$ — must be used once each in any order. You can concatenate these digits to create multi-digit numbers (i.e. $33$). You can use the factorial ...
4
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1answer
1k views

Find three ways of forming the number 100 using 3,3,5,7

As it says in the title. Rules: anything not explicitly allowed is forbidden. use 3, 3, 5, 7 and multiplication, division, sum, difference, unary minus, and exponentiation in any order. Parentheses ...
4
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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 ...
4
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1answer
2k views

I want an exact value of Pi

Use 1, 2, 2, 2 (Each number used exactly once) to form π. I want an exact value of π, not any approximation. Available operators: + - * / ( ) ^ ! You can use any one of them for any times. Hint:...
4
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3answers
364 views

Number wheel Challenge!

Much like the Word-tank-wheel challenge, but numbers! Find a number that can 'rotate' in a way that the origin number and its rotations must be divisible (i.e. whole number) by the number of times it ...
4
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5answers
1k views

The game of Sevens

There is a popular game, named Four fours, where you have to find the shortest mathematical expression for every number from $1$ to $n$, using only the number $4$ and some operators. My variant of ...
4
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2answers
286 views

Numbers and Countries

The relations given below. According to these values, solve the last relationship. Germany - Kenya = 7 Mexico - Brazil = 9 Turkey - Australia = 18 Norway - Ghana = 7 Korea - Japan = 1 Ethiopia - ...
4
votes
4answers
582 views

Find the smallest positive integer that cannot be made from four 8s, or show it doesn't exist

This puzzle was inspired by one recently posted by @Max. What is the smallest positive integer that cannot be made from four 8s, where bracketing is allowed and the only permitted operations are ...
4
votes
7answers
375 views

Sum of three six digit numbers

This puzzle is a variation of a 3 digit addition puzzle I saw recently. A , B , and C are positive integers between 0 and 9. A,B and C are different integers Six digit numbers formed using A,B and ...
4
votes
4answers
582 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 ...
4
votes
2answers
660 views

What's the largest number that can be obtained in the process of solving a numbers game on Countdown?

Countdown is a British game show in which people try and make the longest possible word out of nine given letters, reach a target number using six given numbers and basic arithmetic, and then solve a ...
4
votes
2answers
165 views

What is a Special Prime Number™?

This is inspired by the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles, now with numbers. If a number conforms to a special rule, I call it a Special ...
4
votes
1answer
397 views

Most consecutive positive integers using two 1s

Using two 1s, try to come up with the most consecutive positive integers. Allowed operations: Addition Subtraction Multiplication Division Concatenation Square Root Radical Factorial Floor and ...
4
votes
4answers
740 views

Complete numbers on Clock

I have a different kind of clock at my home. Image of Clock: 5 o'clock on this clock means 1 o'clock actually. Display of data in table: Can you complete all the numbers on this clock by finding ...
4
votes
2answers
337 views

Find the ? in this grid

Find question mark in this grid with numbers. csv version: 9,6,7,3 2,4,7,6 4,1,5,8 3,0,3,? Hint: You use all numbers to find ? and it is much more simple ...
4
votes
2answers
596 views

Uncle's mathematics puzzles after dinner

I was at my grandmother's home for a dinner. With my siblings, after the dinner party, watching a prime time show. One of my uncles, who is a mathematics professor, didn't like and asked us to sit ...
4
votes
2answers
404 views

Arrange numbers 1 to 9 into the upsilon grid

Arrange numbers 1 to 9 into the octagon, so the operation is correct. C is a constant. Do the math operation in sequence, ($×$) and ($/$) is NOT HIGHER than ($+$) and ($-$).
4
votes
1answer
249 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 ...
4
votes
1answer
152 views

Constant puzzle

A constant is hiding behind this puzzle, can you tell which? 4 $\rightarrow$ 2 $\rightarrow$ 1 $\rightarrow$ 1 $\rightarrow$ 1 $\rightarrow$ $\dots$ ? $\rightarrow$ ? $\rightarrow$ ? $\rightarrow$ $\...
4
votes
1answer
212 views

Find the missing numbers in these flowers

Can you figure out the pattern and solve for the three missing numbers? All petals and centers each contain a single digit. There is a unique solution for each missing number. Hint 1: Hint 2:
4
votes
1answer
164 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 ...
4
votes
2answers
420 views

The Six Symbols

The professor turned to me and said, "I believe that all numbers in mathematics can be expressed with only 6 symbols." "A bold claim," I replied. "I suppose the you want all numbers to be encoded in ...
4
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1answer
1k views

Arrange the numbers 1 to 19 in the circles

O---o---O / \ / \ o o o o / \ / \ O---o---O---o---O \ / \ / o o o o \ / \ / O---o---O Arrange ...
4
votes
2answers
319 views

The mathy square strikes back!

This is a follow-up question to Does this mathy square have any solutions? (And how many?). Consider a 7x7 grid of math operators o and numbers ...
4
votes
1answer
227 views

Find pattern for new equation in number sequence

I saw this puzzle on this address. $3+5+7=152181$ $4+5+6=202461$ $3+4+7=122172$ $9+4+5=364518$ $8+6+8=?$ I know that first $4$ digits are $4864$. How could I find last $2$ ...
4
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2answers
1k 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 ...
4
votes
1answer
174 views

Draw out a Battle!

I'm thinking of a number. It's 5 digits long There's a 5 between a 7 and a 2. The second-biggest number is on the far right. The average digit value is equal to the second-lowest digit. The smallest ...
4
votes
1answer
524 views

Arrange numbers and operators to the magic triangle

Note : A # B = A*10 + B Arrange the numbers 1 to 9 to green triangles, and arrange operator (+,-,x,/,^, and #) to the white triangles, so the math operations below are equals. (((A op1 B) op2 D) op3 ...
4
votes
3answers
416 views

Arrange numbers to a 6 point star

Arrange the numbers (1,2,3,4,5,6,7,8,9,11,12, and 16) to replace the letters, so every 3 vertices which form a triangle have equal sums.
4
votes
1answer
176 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 ...
4
votes
1answer
197 views

Numbers in the wheel

Arrange the numbers 3 to 27 onto the wheel using these rules: The modulus of two adjacent numbers must equal with the number between them. Modulus here means the remainder when the bigger number is ...
4
votes
2answers
212 views

Representation of Mo-roman numerals

This continues the spirit of Mo-roman numerals started by humn What is/are the natural number(s) that has/have the most different representations in mo-Roman numerals and what is the number of ...
4
votes
1answer
358 views

A challenging Magic Square

Find a 3x3 Magic Square where each row, column and both diagonals result in positive number 9 You are allowed any of the 4 math operations : add, subtract, multiply or divide. NO OTHER OPERATIONS ...
4
votes
1answer
185 views

Numbers at a flower-like circles

Above picture is a flower-like circles with digits to each intersection which follow the rules: A circle and its center must contain all of the digits from 1 to 7. I have put some numbers to some ...
3
votes
10answers
19k views

Make numbers 1-30 using 2, 0, 1, 9

This is very similar to the 2, 0, 1, 8 problem. Just try to make all numbers 1-30 using the digits 2, 0, 1, 9. Rules: Use all four digits exactly once Allowed operations: +, -, x, ÷, ! (factorial), ...
3
votes
5answers
4k views

Minimum difference with Digits

You have digits from $0$ to $9$, where you have to use every digit only once. create 2 numbers from the digits so the difference is minimum. example : $30568 - 29471 = 1097$ What is the lowest ...
3
votes
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 ...
3
votes
4answers
725 views

Make numbers from 1-10 with 5 3s

In this puzzle book, I came across a question that goes like this: Make the numbers from 1-10 using 5 3s. Rules: You are only allowed to use the four basic arithmetic operators ($+, -, \times, \div$...
3
votes
2answers
585 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 ...
3
votes
3answers
291 views

Puzzling Number Boxes

Found this puzzle as a translation question. The Chinese is fairly simple, it just asks to solve for the ? in the bottom right square. The actual puzzle though, I have no clue about. Can any of you ...
3
votes
2answers
760 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 ...
3
votes
4answers
367 views

Numbers at the corners of concentric squares

Put 4 distinct 1 digit non-negative numbers (A, B, C, D) to every vertex of a rectangle. Then put the last digit of the sum of 2 connected vertexes at the sides of the rectangle. Create smaller ...
3
votes
2answers
3k views

Finding the largest 7-digit number

Find the largest 7-digit number without its digits repeating, such that the number is divisible by all of its digits I found some constraints: • 0,4 and 5 cannot be included • The number found should ...
3
votes
1answer
521 views

Find the rule : triplet number into Positive Integer

These are triplets of numbers into positive integers: ...
3
votes
1answer
604 views

Can you find the pattern?

If the following are true: $4+7+2 = 281435$ $7+3+9 = 212781$ $6+2+7 = 121456$ $2+8+5 = 164036$ Then what would the following equal? $8+4+6\ =\ ?$ Can anybody check my work? I think the answer is:
3
votes
1answer
145 views

Fill each blank with a digit 1-9 without any repetition [closed]

Fill the following place holders with digits in the range from 1 to 9. Each digit only appears once and make the equation sum up to 100. _ /_ * _ + _ * _ * _ / _ + _ * _ = 100 Also, what is the ...

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