Questions tagged [formation-of-numbers]

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

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12
votes
3answers
660 views

Who will find the number on their own hat first?

Both $A$ and $B$ have numbered hats on their heads. $A$ and $B$ both cannot see his/her own hat, but they can see other one's hat. $A$ sees number on $B$'s hat as $5$ and $B$ sees $A$'s number as $4$. ...
7
votes
5answers
7k views

Alternating numbers

Alternating numbers are numbers in which all digits alternate between even and odd. For example: 2703 and 7230 are alternating ...
2
votes
1answer
152 views

decipher this modified sum operation,

This is crossposted from Math.SE, the original question is here $1+2+3+4 = 61$ $2+3+4+5 = 52$ $3+4+5+6 = 51$ $4+5+6+7 = 50$ $7+8+9+10 = ?$
29
votes
13answers
14k views

10 9 8 7 6 5 4 3 2 1 = 2016

Add the four basic operators $\times\div+\,\;-$ and optionally brackets to: $10 \quad 9 \quad 8 \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1$ To get the total $2016$. Rules: We are ...
-7
votes
5answers
305 views

Largest number with two hands [closed]

Pretty short one, really. Given your two hands, what's the largest number you can represent? Some example representations: 1 finger on each hand: that's 2. 2 fingers on one hand, and 3 on the other: ...
-3
votes
2answers
2k views

Fill in the operators to make $7 \circ 8 \circ 7 \circ 7 \circ 8 \circ 3 = 100$

With the given numbers I need to make: $7 \circ 8 \circ 7 \circ 7 \circ 8 \circ 3 = 100$ Using only the following operators: $+\space-\space\times\space\div$
3
votes
0answers
306 views

How is it possible to make 8 (…) 8 (…) 8 = 6? [duplicate]

$$8\text{ }8\text{ }8 = 6$$ Add in any required number of mathematical symbols to make the above equation work. How is this possible? Can somebody explain?
4
votes
2answers
198 views

Autonumerograms

An autonumerogram, or self-enumerating number, is a number that can be read as describing itself by providing a pairwise inventory of its own digits. For example, 22 (two 2's) and 14233221 (one 4, two ...
8
votes
1answer
2k views

A basic calculator, a simple game. What was I playing at? [duplicate]

Yesterday I was doodling around with my very simple calculator as shown in the picture. First I would enter a few digits to make an integer (i.e. no decimal places). Then I would perform a simple ...
18
votes
3answers
2k views

Puzzling 101: Sums of seventeen numbers

After reading a bit in Meta and the help section, I'm still not sure whether this qualifies as a "good" puzzle in the spirit of the site, but the votes will show - I liked it when I encountered it, ...
5
votes
3answers
3k views

Express the number $2015$ using only the digit $2$ twice

Can you use only two instances of the digit $2$, along with the mathematical operations below, to create an expression that evaluates to $2015$? Allowed operations: arithmetic operations: addition ($...
2
votes
1answer
204 views

Depressed Numbers [duplicate]

$12 = 0$ $1234 = 1$ $123456 = 2$ $12345678 = 4$ $369 = 2$ $248 = 3$ $2 = 0$ $3 = 0$ $5 = 0$ $7 = 0$ $11 = 0$ $13 = 0$ What does: $123456789 = ?$ Why? Hopefully isn't too hard, please ask if you ...
14
votes
4answers
480 views

A Perfectly Primitive Parameter Permuter

A simple challenge for the mathematically inclined. Find a function $f\left( {{x_1},{x_2},{x_3},{x_4}} \right)$ such that $$\begin{gathered} f\left( {2,3,4,5} \right) = 1 \hfill \\ f\left( {1,3,4,...
-4
votes
1answer
861 views

Using the digits 2, 3, 4 make an expression for 30

Write an expression using exactly one 2, exactly one 3, and exactly one 4 to make 30. For each problem, you must use all three of these: Division Factorials (just for regular factorial use, no ...
-5
votes
2answers
1k views

Make 24 and 30 using the digits 3 and 4

First, write an expression using exactly one 3 and exactly one 4 to make 24. Second, write an expression using exactly one 3 and exactly one 4 to make 30. Math You Can Use for each problem: ...
7
votes
4answers
2k views

A Threes Of Cake

This question is similar to my other question Twos For Thought, which arguably was a better pun but I decided to recreate the question, except with threes! How many threes do you need to get to the ...
4
votes
4answers
574 views

Twos For Thought

How many twos do you need to get to the number $100$ exactly? Example: $22+22+22+22+2^2+2^2+2^2$ This example method uses 14 twos and is obviously not ideal. Can you find a way that uses the least ...
2
votes
3answers
252 views

Number formation with digits given

How do you form the number 1000 with the digits, 1,2,3 and 4? The mathematical operations that can be are addition, subtraction, multiplication, division, parentheses, percentages and factorials. ...
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
539 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 ...
70
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 ...
14
votes
12answers
265k 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 ...
44
votes
10answers
148k 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
766 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
11k 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
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 ...
4
votes
2answers
574 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 ...
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 ...
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 ...