Questions tagged [formation-of-numbers]

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

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-3
votes
1answer
163 views

Make 100 with only 9 numbers [closed]

Make 100 with ONLY 9 numbers Hint 1: Hint 2: Hint 3: Hint 4:
10
votes
4answers
887 views

Making the whole set into primes

Let's say you start with a set of sequential integers starting from 2, so: $ 2, 3, 4, 5, \dots, N $ for some $ N > 2. $ The goal is to use identical basic arithmetic operations ($ +, -, \times, \...
6
votes
2answers
289 views

Building the perfect number 28 with fractions

You are given the fractions $\frac{4}{3}, \frac{7}{3}, \frac{10}{3}, \frac{13}{3}.$ Use any operation of $+, -, *, /, ()$ to build 28 with those four fractions. You must use all four fractions ...
7
votes
1answer
277 views

Building the perfect number 28 with fractions - part2

Here is a follow up of Building the perfect number 28 with fractions You are given the fractions $\frac{3}{2}, \frac{5}{2}, \frac{7}{2}, \frac{11}{2}.$ Use any operation of $+, -, *, /, ()$ to build ...
7
votes
9answers
3k views

Creating 123456 in the fewest number of steps

You start with the number 1. You can create a new number by applying an operation on two existing numbers (can be the same). The operations are +, - and *. What is the fewest number of steps needed to ...
3
votes
6answers
1k views

Make 28 with the numbers 2020

Try to make 28 from the numbers 2020. Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root, squaring, parentheses.
-5
votes
1answer
205 views

Make the numbers 1-50 using 2, 0, 2, 0

Make the numbers 1-50 using 2 0 2 0 in the given order. Use all four digits exactly once. Allowed operations: +, -, x, /, ! (factorial), double factorial, exponentiation, square root, parentheses. ...
2
votes
2answers
172 views

Make numbers 1-50 using $\pi$ and its digits (but with some penalties) [closed]

In this problem, you will be allowed to use some operations and additional digits from the basic approximation of $\pi=3.14$ having some penalties, as follows: Operations: Using basic operations and ...
2
votes
1answer
124 views

Make $\pi$ using 2 0 2 0 in this order

How can you make $\pi$ using 2, 0, 2, 0 in this order? Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, parentheses.
9
votes
3answers
2k views

$\tau$ is greatest! $\tau$ is all (from 1 to 20)

(This is basically an extension of $\pi$ Day puzzle one to twenty) $\tau$ is greater than $\pi$ and $\tau>\pi$. Create the numbers from $1$ to $20$ using only: Tau ($\tau$, equivalent to $2\pi$) ...
-4
votes
3answers
201 views

Ten, nine, eight, seven, six, five, four, three, two, one

Some of us already did, and some of us are going to end the years with the word "teen" in it soon, for another 94 years. So let me ask the question: How many distinct numbers can you produce with ...
3
votes
1answer
334 views

Four dice puzzle: Postscriptum

This continues (and completes) the sequence of four dice puzzles: Four dice puzzle: 2,2,4,5 Four dice puzzle: What's the best throw? The days go by and Damiano is still throwing his four dice. He ...
9
votes
1answer
391 views

Four dice puzzle: What's the best throw?

This continues Damiano's puzzle "Four dice puzzle: 2,2,4,5" Damiano keeps throwing his four dice. After a lot of throwing and thinking and working, he has determined for every throw $a,b,c,d$ of his ...
8
votes
2answers
666 views

Four dice puzzle: 2,2,4,5

Damiano has thrown four dice and the numbers 2, 2, 4, 5 showed up on top. Damiano asks himself: What is the smallest positive integer that cannot be generated with these four numbers according to ...
-2
votes
1answer
104 views

123456789 = 100 with three operations? [duplicate]

Given the sequence 123456789 You can insert three operations (+,-,X,/) into this sequence to make the equation = 100. Is there a way to solve this without brute force?
16
votes
2answers
1k views

A geometric sequence using one digit

Give the first few terms of a geometric[1] sequence such that: the sequence is increasing and infinite only one digit is used throughout the sequence the terms are written as base ten ...
12
votes
3answers
1k views

Fill your bucket with 2020

You are given two buckets. These buckets are a bit weird, for the only thing they can hold are numbers. One is empty, but the other one contains numbers $1,1,2$. Your goal is to get the number $2020$ ...
1
vote
4answers
232 views

Can you reach 2020?

Start with the numbers 1,2,3,4,5,6,7,8,9,10 in that order and use the four common operations (+ − × ÷) and number concatenation (ie, you may write 123 concatenating 1, 2, 3) to obtain 2020....
8
votes
5answers
5k views

smallest number obtainable from 2020

If only the four basic operations, concatenation and parenthesis are allowed, the largest number which can be obtained from $2$ $0$ $2$ $0$ is... $2020$ :-) (If exponentials were allowed, $20^{20}$ ...
71
votes
15answers
13k 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
2answers
1k views

Euler's identity

Warning: this question requires knowledge of complex numbers. An Euler's identity is an identity, in which each of the following appears once and only once: the constant $0$: neutral element for ...
-4
votes
1answer
103 views

How do I solve this puzzle?

I am trying to answer this puzzle - which of the five potential answers is correct, and why? This test comes from Metropol iq1 book
0
votes
2answers
102 views

How do I solve this numerical puzzle?

I am trying to answer this numerical puzzle - which of the five potential answers is correct, and why? 6*3*5 = 183033 5*4*3 = 201532 7*2*7 = 144928 8*2*9 = ? ...
4
votes
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:...
7
votes
4answers
607 views

How to make the number 49?

You've to start with $1$ and can use each of the following operations at most once. You can do the following in any order you like: 1) Add $2$. 2) Add $3$. 3) Add $5$. 4) Multiply $2.$ 5) ...
-3
votes
2answers
224 views

What is the next number in the sequence and why?

7 4 11 2 14 5 18 3 21 ? Find the next number in the sequence?
3
votes
2answers
209 views

SAME DIGIT NUMBER PUZZLE

You have 5 numbers 1, 9, 3, 5, and 7 you need to arrange these number like Rules create 2 pairs from numbers above keep one of the number in the middle then apply this law ...
6
votes
3answers
644 views

Number Equation Matrix

Can somebody please solve this? My daughter's school teacher gave her this puzzle to solve at home. But to me it seems a little out of order, and that's why I am asking here for help.
1
vote
1answer
96 views

Find the missing number (number sequence puzzle) [duplicate]

Find the missing number 56784 = 4 11111 = 0 72348 = 3 88652 = 5 88811 = 6 75213 = 0 65465 = 3 62257 = ? I found this quiz in an archive of our company's ...
1
vote
3answers
2k views

Make 38, 44, 46 using 2,3,8,7?

Using BODMAS/BIDMAS* and the numbers and signs 2,3,7,8, (), -,+,÷,× can you make 38, 44, 46. You can only use each number once. I can't figure it out myself Brackets Order Division Multiply Add ...
12
votes
16answers
5k views

Make 2019 with single digits

This puzzle is inspired by a puzzle by @Andrew, where the goal is to make 1998 from a minimal amount of 8s. This is a variation of the puzzle, where the goal is to make 2019 using a minimal amount of ...
-3
votes
2answers
147 views

How do you make 29 only using the numbers 1 2 3 4 [closed]

How do you make 29 with only using the numbers 1 2 3 4? I have tried a lot of solutions and please remember that you can't use the number 5
45
votes
10answers
150k views

1 2 3 4 5 6 7 8 9 = 100

The sequence of numbers $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9$ has the property that you can insert mathematical operators in between the numbers from $1$ to $9$ and make the expression evaluate to 100. For ...
32
votes
18answers
11k views

Use 2, 0, 1 and 8 to make 109

Assemble a formula using the numbers $2$, $0$, $1$, and $8$ in any order that equals 109. You may use the operations $x + y$, $x - y$, $x \times y$, $x \div y$, $x!$, $\sqrt{x}$, $\sqrt[\leftroot{-2}\...
62
votes
24answers
20k views

Make 0 0 0 0 = 8

Can you find a way to make: $0\ 0 \ 0 \ 0 = 8$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
21
votes
12answers
5k views

Make 1998 using the least possible digits 8

Make the number 1998 using the minimum amount of digits 8. Your allowed operations are +, -, *, /, ^, % (percent). You need not use only integers 8: 88 and the likes are acceptable. You must only ...
5
votes
4answers
197 views

Find 2018 with the least amount of numbers

Can you assemble a formula using the least amount of one digit numbers (from $0$ to $9$) so that the results equals to 2018 with the rules below? You may use the operations $x + y$, $x - y$, $x \...
14
votes
4answers
1k views

Squares inside a square

Distribute the digits from 1 to 9 to a 3x3 square, such that you reach as many square numbers as possible. A valid square number in the 3x3 square is either a single digit square number or is build ...
4
votes
1answer
209 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 $2$ ...
10
votes
1answer
193 views

Make $2471$ out of first seven powers of two

Can you make $2471$ using first seven powers of two: $1,2,4,8,16,32,64$, each exactly once? Only the basic operations are allowed: $+,-,\times,\div$, and parentheses $(\space)$. ...
14
votes
3answers
1k views

How many consecutive integers can you make using only four digits?

In the spirit of the classic four fours, I wonder what's the optimal set of four numbers? Your goal is to make the most consecutive integers using four digits of your choice. Pick four: $0,1,2,3,...
12
votes
6answers
728 views

Use 0 1 2 3 4 to form 9 3-digit numbers

Use $0, 1, 2, 3, 4$ to make the any of these numbers: $$331, 333, 435, 452, 455, 458, 461, 469, 470$$ You must use all $5$ digits $0, 1, 2, 3, 4$ each exactly once. You can make multi-digit ...
8
votes
3answers
5k views

How to make 21?

How do you make $21$ from the numbers $1$, $5$, $6$, and $7$? You can use the operations of addition, subtraction, multiplication and division, as well as brackets. You must use each number exactly ...
6
votes
1answer
171 views

How to make the two important years 1492 and 1969 with a minimum number of 1s

Using only 1s, make 1492 and 1969 with the minimum number of digits Rules: allowed operations +, -, ×, ÷, ^, (), and ! (factorial). Concatenation of the original digits is allowed, but not (1+1)1=21. ...
2
votes
10answers
16k 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), ...
7
votes
1answer
178 views

How do you make 66 using three 4s

Rule: allowed operations: +, −, ×,/,^,√, and ! (factorial) example: 4^4+4!=280
11
votes
6answers
2k views

Some interesting calculation puzzle that I made

So I'm creating some kind math puzzle that goes like this: 1=-2+3 12=3*4 123=(4*5)+(6+7)*8-9+10 (thanks JS1 for finding shorter one) 1234=(5*6*7*8)-(9+10+11+12+13+14+15+16+(17*18)+19+20+(-21+22)) ...
2
votes
3answers
227 views

IQ test sample patterns. Can anyone find the missing number? [closed]

I am fully hopeful that you can crack this puzzle. You need to answer with an explanation.
4
votes
3answers
240 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 ...
0
votes
1answer
90 views

Puzzle on a blackboard [closed]

What is the missing number in the picture above?(question is from some puzzle game) I tried some approaches, but haven't found any meaningful rule..thanks in advance!