# Questions tagged [formation-of-numbers]

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

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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 ...
145 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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
900 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) ...
222 views

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 $... 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 ... 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 ... 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 ... 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 ... 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 ... 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? 1answer 65 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 ... 1answer 94 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 ... 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 ... 2answers 11k views ### Make 10 out of 1, 1, 5 and 8 A friend of mine shared a puzzle with me this evening. Using the numbers 1, 1, 5 and 8 exactly once, and the basic operations (+, -, /, *) and (optionally) parentheses, form an expression which ... 4answers 1k views ### A mazegic square So you like mathematical diversions? Here's something new for you then ... 3answers 714 views ### Use 2,3,4,5 to get 26 using only + - * / Use 2,3,4,5 and + - * / only once each (it's not necessary to use all of them) to equal 26. I know 2 answers, but there is a 3rd (or more) :) 1answer 297 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 ... 2answers 271 views ### When is my date of birth? ___4,_4,_4 This is my real date of birth, because it looks unique, I try to do a simple operation, and I get a number 222. In fact it is able to solved without looking at the hint, but I'm trying to ... 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 ... 6answers 25k 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: + - * / ^ ("^" ... 12answers 266k 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 ... 2answers 234 views ### Factor the number 23 into four numbers$a + b \sqrt{2} + c \sqrt{3} + d \sqrt{6}$[closed] We know that$23$is a prime number nonetheless, I'm asking to find 4 numbers$a,b,c,d > 0$such that$23$factors. $$23 = A \times B \times C \times D \text{ with } A,B,C,D = a + b \sqrt{2} + c \... 4answers 4k views ### Get 59 from 1,9,4,8 in order [closed] I’m stuck on trying get 59 by the numbers 1,9,4,8 in order. I have no idea if it’s possible, I made it for 1-70 just not 59. I made it without order: (-1+8)*9-4 You can use not only the basic ... 2answers 269 views ### Making 30 using 3 3s [closed] Hope that all can answer the question. It's an IQ! How can one make 30 using 3 only three times? 4answers 331 views ### find out the missing expressions [closed] 10 10 10 10 = 1 10 10 10 10 = 2 10 10 10 10 = 3 10 10 10 10 = 4 10 10 10 10 = 5 10 10 10 10 = 6 10 10 10 10 = 7 10 10 10 10 = 8 10 10 10 10 = 9 10 10 10 10 = 10 You can only add ... 2answers 614 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? 3answers 280 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 ... 1answer 494 views ### What is the smallest counting number you can create higher than 1? [closed] What is the smallest integer you can create using 1,2,3,4,5,6,7,8,9 that is strictly greater than 1? You can use any mathematics symbol. You must use all nine numbers. You can't use the same number ... 4answers 691 views ### (addition) 7 point star / heptagram Place the numbers 1 through 14 onto each point, so that: A = 1 The sum of points in every line are equal, (A+I+J+C = B+J+K+D = C+K+L+E = D+L+M+F = E+M+N+G = F+N+H+A = G+H+I+B) A+B+C+D+E+F+G+1 = H+... 2answers 281 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 - ... 3answers 2k views ### Mathematics IQ puzzle, solving puzzle by looking at neighboring digits [closed] Can anyone solve this puzzle? I have tried many times but I could not find any symmetry or sequence. \begin{array} {|c|c|c|} \hline 3&25&5\\ \hline 16&9&6\\ \hline 125&36&18\\ ... 2answers 1k views ### Pick seven numbers so that every operation gives same result Pick seven numbers so that every operation (addition, subtraction, multiplication, but not division) gives the same result. For subtraction, you may take the result's absolute value. Numbers cannot ... 1answer 877 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: ... 3answers 3k views ### A breathtaking way of making every possible positive integer This is a follow-up question to my older puzzle "A truly amazing way of making the number 2016" and to my other older puzzle "A truly amazing way of making every possible positive integer". My ... 1answer 160 views ### What is the relation between these numbers? Based on the relation between the numbers of each shape, find the number for the question mark. 337 339 549 569 Source: Iraninan Ph.D University Enterance 2017 9answers 2k views ### How to use the numbers 3, 5, 6, and 7 to get 100? [closed] Any mathematics symbols and processes to use the numbers 3, 5, 6, and 7 once each to get 100. 1answer 410 views ### What is the minimum number of digits required to make the numbers 1-20? What is the minimum number of digits required to make the numbers 1-20? Any n consecutive numbers can be counted as a n-digit consecutive number. So,$$12\\34$$has the numbers$$1, 2, 3, 4, ... 3answers 1k views ### Two functions that can't be applied in different order to arrive at same result Here's my puzzle: Write two unary functions f, g and provide an input x so that only the ... 5answers 3k views ### Make 2008 from Φ (Golden Ratio) I know that questions of the form "Use [arbitrary set of numbers] to make 2018" seem to be not very well recieved in the last days. That's why this puzzle is about making 2008. But instead of using ... 2answers 475 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 ... 3answers 278 views ### Integers around a circle with consecutive pairs differ to a square Inspired by this puzzle : Integers around a circle with consecutive pairs adding to a square The integers 1 to 50 are placed around a circle in such a way that the difference of any two of them which ... 4answers 1k views ### Use four 8's to make the number 2016 Previous question: Use two 2's, two 1's, and two 8's to make the number 2018 Background: I was trying to add some new elements (hopefully creative and interesting) to this traditional type of number-... 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{\...
I and Ron were talking casually over coffee. Just then a thought sprung into my mind; could there exist numbers such that if their digits are reversed, for example $123\to321$, the new number is ...