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Questions tagged [formation-of-numbers]

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

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14
votes
12answers
264k 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 ...
0
votes
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 \...
8
votes
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 ...
-2
votes
2answers
252 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?
-6
votes
4answers
322 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 ...
15
votes
2answers
609 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?
3
votes
3answers
276 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 ...
-4
votes
1answer
459 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 ...
6
votes
4answers
673 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+...
4
votes
2answers
280 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 - ...
5
votes
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\\ ...
7
votes
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 ...
8
votes
1answer
873 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: ...
9
votes
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 ...
1
vote
1answer
158 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
2
votes
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.
55
votes
13answers
12k views

Making π from 1 2 3 4 5 6 7 8 9

There have been two other questions here and here that are similar to this one, but this changes the rules up a little. Your job is to approximate $\pi$ using the sequence of digits (in order): 1 2 ...
5
votes
1answer
376 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, ...
10
votes
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 ...
13
votes
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 ...
5
votes
2answers
464 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 ...
7
votes
3answers
276 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 ...
8
votes
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-...
12
votes
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{\...
3
votes
0answers
205 views

Find the combination algorithm for 16 digit numbers [closed]

Find the combination algorithm for numbers that will be generated. And the numbers are: 0535 8549 9933 3564 0500 7197 6709 9534 0531 3170 7802 8731 The numbers ...
8
votes
2answers
7k views

Is Ron a mathematical prodigy?

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 ...
6
votes
4answers
5k views

Can you make 2 0 = 1 5? [closed]

Can you find a way to make 2 0 = 1 5 by adding any operations or symbols? You can use symbols such as these: +, -, *, !, ^, (). It is not limited to this list.The symbols may be added either between ...
5
votes
8answers
4k views

How to use 2,0,1,8 to make 51? [closed]

How to use the number 2,0,1,8 to make 51? You can use any operation except for multiple factorials and you can concatenate numbers, ex.2,0=>20 You can take the square root of a number without a ...
-5
votes
3answers
188 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 ...
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
1answer
140 views

From the information given below- prove that Z = 4561

If- ONE * THREE * FIVE = 225 NINE * SEVEN + TWELVE = X 225 + X = Y 10,18,32,56,93,146,? ? + Y = Z Prove that, Z = 4561
-2
votes
1answer
196 views

What is the next number in the integer sequence?

What is the next number in the following sequence? 25 27 30 34 39 45 52 60 69 79 69 60 52 45 39 34 30 26 22 18 82 78 74 70 66 67 64 60 65 80 ?
7
votes
1answer
481 views

Two Christmas trees

To each Christmas tree : Put two $+$, two $-$, and two $×$, to the yellow triangles. in a row, there must be different operators (so between $[2,0,1,7]$ all $3$ operators must appear) $A - B$ means $|...
4
votes
4answers
602 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
1answer
188 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 ...
33
votes
5answers
7k views

Rendering the number 10,958 with the string 1 2 3 4 5 6 7 8 9

Brazilian mathematician Inder Taneja has found a way of expressing every number between 1 and 11,111, except 10,958, by inserting mathematical operators in between the numbers 1 2 3 4 5 6 7 8 9 and ...
-5
votes
2answers
121 views

Expressing numbers as sum of two squares and two powers of 2

It has been shown that the smallest integer, greater than 1, that cannot be represented as a sum of two squares and at most two powers of 2 is 535,903. Show how to express 535,902 as the sum of two ...
19
votes
5answers
6k views

How to get 5 from 0,0,0 and 1?

Can you use the digits 0,0,0 and 1 each only once in a mathematical expression for the number 5 using only common mathematical symbols with at least 1 mathematical symbol between each number?
3
votes
5answers
3k 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 ...
1
vote
4answers
460 views

Finding pattern of numbers

I have this puzzle for adding 2 numbers (Or sequences) Does anyone have an idea about how this addition works? $$ 5+1=9\\3+1=10\\5+2=21\\8+2=23\\9+0=28\\4+3=?? $$
-2
votes
1answer
370 views

Make numbers 1-31 with 1,9,7,8

I am stuck with some of the solutions. These are rules: Use all four digits exactly once Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root, squaring, parentheses Thank you ...
3
votes
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. ...
2
votes
0answers
363 views

Number sequence with two missing numbers 15, 39, 1/8, 1/49, 100, 11, _, _

Given the following incomplete number sequence: 15, 39, 1/8, 1/49, 100, 11, __, __ What are the two missing values?
17
votes
2answers
13k 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 ...
7
votes
6answers
2k views

How can you get 125 from 2,3,4,5,6?

You are allowed to use the four standard operations (+-/*) to get 125, using each of the following digits exactly once: 2, 3, 4, 5, and 6. I came up with an answer, but took me a while; curious to ...
30
votes
1answer
761 views

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 sum of any two of them which are adjacent is a perfect square. Of these integers, the even numbers are then removed. Restore them....
4
votes
2answers
324 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
573 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
1answer
153 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 ...
2
votes
5answers
956 views

Make 12 with 1, 5, 19, 10

How can you make the number 12 with just the numbers 1,5,19,10? You can only use each number once, and can only use subtraction addition multiplication and division.