# Questions tagged [formation-of-numbers]

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

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### 876925431=2016 Use the four basic operators

Use the four basic operators ×, ÷, +, − and if you want brackets to make: 8 _ 7 _ 6 _ 9 _ 2 _ 5 _ 4 _ 3 _ 1 = 2016. You can use each operator as many times as needed. Concatenation is not allowed.
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### Math Challenge: Create 8

Using only $2$, $7$, and $7$ (each one must be used only once) and only using the operations $+$, $-$, $\times$, $\div$, $\textrm{^}$, and parentheses, make 8. You can also use decimals.
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### Smallest Unattainable Target in Letters and Numbers (Countdown in the UK)

To cheer myself up during the twin problems of (1) underperforming sports team XXX and (2) lockdown in state YYY, neither of which shall be named, I am doing daily number puzzles based on the show ...
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### There are $3$ boxes with total $27$ balls. Find minimum number of steps to get to equal balls in each box

You have $3$ boxes $A, B$ and $C$. Boxes $A$ and $B$ are empty to start with and box $C$ has $27$ balls. In "$i$-th" move you make, you must transfer exactly "$i$" balls from one ...
429 views

### Can you find the number?

There's a number with the following characteristics: The hundreds digit plus the units digit minus the tens digit equals 8. 3 times the hundreds digit plus 2 times the tens digit minus the units ...
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### too easy puzzle? Try it first!

Arrange the numbers $1$ to $9$ to replace letters $A$ to $I$ so: $(A+B+C+D)-(E+F+G+H) = I$ Too easy? Too many answers? Try it first! Then explain why.
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### Formula One (?) Hard Puzzle

On a website I use to go, one of the writers gave this hard puzzle: What are the meaning of those numbers given they are not Norwegian coordinates. 60.6604211,10.7210713 I have no clue how to solve ...
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### 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:
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### 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 ...
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### 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 ...
179 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 ...
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### 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.
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### 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. ...
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### Make 28 with the numbers 2020

Try to make 28 from the numbers 2020. Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root, squaring, parentheses.
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### 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 ...
334 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?
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### A geometric sequence using one digit

Give the first few terms of a geometric sequence such that: the sequence is increasing and infinite only one digit is used throughout the sequence the terms are written as base ten ...
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### 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 $2020$ ...
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### 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....
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### 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 ...
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### 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, $20^{20}$ ...
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 ...