Questions tagged [formation-of-numbers]

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

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6
votes
3answers
2k views

What numbers fill the blanks to satisfy the equation?

Complete the grid shown below with the digits 1 to 6 to make the sum correct. Perform each mathematical operation in the order shown, from left to right, e.g. 1 + 2 x 3 is treated as (1 + 2) x 3 = 9. ...
-2
votes
5answers
531 views

Form a number using some numbers and mathematical operations

Using 2,3,4,5,6,7 and basic mathematical operations form the number 1088. Every digit must be used exactly once (neither zero nor greater than one times). Concatenation of digits (such as 53) is not ...
-4
votes
2answers
212 views

Using numbers form a number

Using 7,8,9 and basic mathematical operations form the number 327600. Use every digit exactly once. Note: Allowed Operations: $+,-,/,*, {}^{\displaystyle\large\hat{}} ,!,\sqrt{}$
4
votes
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 ...
54
votes
13answers
11k 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 ...
14
votes
12answers
263k 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 ...
43
votes
10answers
142k 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 ...
5
votes
3answers
5k views

Create integers from 1 to 50 using only one integer and other functions

Your task is to create all the integers from 1 to 50 (inclusive) using only a single integer $x$ and... Addition ($+$), Subtraction($-$), Multiplication($\times$), and Division($\div$) Floor($\left \...
8
votes
2answers
1k 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 $2\pi$) ...
8
votes
3answers
1k views

$\pi$ Day puzzle one to twenty

Create the numbers from 1 to 20 Using $\pi$ Normal arithmetic operation $+ - * /$ Square root $\surd$ Exponential $(X^Y)$ Negative() minus sign $-$ Floor() function, express between $[ x ]$ $[ ...
12
votes
3answers
745 views

Replace each ? in the expression with a digit or operator

In the following expression, replace each ? with either a digit or an operator: 8?5+??5-9?+3 so that it can evaluate to: <...
24
votes
4answers
10k views

The largest integer made of 1,2,3,4

What is the largest integer $A$ that can be produced from the four digits $1,2,3,4$ subject to the following rules? Each of the digits $1,2,3,4$ is used exactly once. Juxtaposition of digits is ...
34
votes
4answers
3k views

Display a number using a scientific calculator with most keys are stuck

Your have a scientific calculator such that most of the keys are unable to be pressed. The only keys that work are those for the functions $$ x^2 \;\; \sqrt{x} \;\; x!\;\; \exp\;\; \ln\;...
8
votes
3answers
4k 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 ...
4
votes
2answers
568 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 ...
13
votes
5answers
3k views

What is the smallest positive integer, which can not be written without repetitions of digits and using arithmetics only?

Suppose you are allowed to use all 10 digits (0,1,2,...9) at most once each; 4 arithmetic operations ($-$,$+$,$\times$,$\div$), each any number of times; parenthesises to group operations; and you can ...
16
votes
2answers
12k 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 ...
4
votes
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 ...