# Can you generate '1' using only 5 and 4 ?

You can use any Mathematical expression,any method suitable...stupidity is on.

But the challenge is you cannot use any other numbers,you can use 5 and 4 only once and you cannot use '-'(minus) sign.

I know 4 possible methods...Can you find still more ?

Note by Vinay Sipani
6 years, 11 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
• Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

## Comments

Sort by:

Top Newest

The four solutions that i know are:

1. The most basic: Tan(45)=1
2. 5%4=1 which is same as remainder when 5÷4
3. $\Im^{4}=1$,where $\Im$ is imaginary number.
4. Condone me after reading this...

$\text{FIVE in Roman = V;}$ $\text{FOUR in Roman = IV.So,}$ $\frac{4}{5}=\frac{IV}{V}=I=1$

- 6 years, 11 months ago

Log in to reply

$5^{\mu(4)}$ is also posible, where $\mu$ defines the MOBIUS function.

- 6 years, 10 months ago

Log in to reply

Yes...thats right👍👍 Good use of MOBIUS function

- 6 years, 10 months ago

Log in to reply

even cotan(45)=1

- 6 years, 11 months ago

Log in to reply

yup..right.👍👍

- 6 years, 11 months ago

Log in to reply

even cot(45)=1

- 6 years, 11 months ago

Log in to reply

5 (mod 4) = 1

- 6 years, 4 months ago

Log in to reply

5-4=1

- 6 years, 6 months ago

Log in to reply

$\frac{d}{dx}(x+54)=1$

- 6 years, 4 months ago

Log in to reply

Woahh, allaww

- 6 years, 11 months ago

Log in to reply

Same thing as 5-4 but looks different $\int _{ 4 }^{ 5 }{ dx } = 1$ Lol. X'D

- 6 years, 11 months ago

Log in to reply

yess....even this is possible👍👍

- 6 years, 11 months ago

Log in to reply

Nicely done, didn't see that.

- 6 years, 11 months ago

Log in to reply

$\dfrac { Gamma(5) }{ 4! } =1$

- 6 years, 11 months ago

Log in to reply

Could u explain what the gamma() function's purpose

- 6 years, 11 months ago

Log in to reply

The factorial $n!$ is originally defined only for positive integers $n$, so 18th century mathematicians came up with an integral $Gamma(t)=\Gamma (t)=\int _{ 0 }^{ \infty }{ { x }^{ t-1 }{ { e } }^{ -x }dx }$ that has properties similar to the factorial, but defined for all real and complex numbers $t$ (except $0$ and negative integers). It works out that $\Gamma (t)=(t-1)!$. A very versatile function, the gamma function is one of the most widely used functions in mathematics.

- 6 years, 11 months ago

Log in to reply

Woah!!!...thank you so much!!!

- 6 years, 11 months ago

Log in to reply

Mike, Don't you think the expression Gamma(t) = (t-1)! still has - which contradicts the basic condition.. Excellent knowledge though

- 6 years, 11 months ago

Log in to reply

Aw yes. :-)

- 6 years, 11 months ago

Log in to reply

yeah...never thought of this...👌👍

- 6 years, 11 months ago

Log in to reply

Can you please tell me what is it's actual meaning? Like 8! means 8(8-1)(8-2)......(8-7) so what is the meaning of -2! ?? @Michael Mendrin

- 6 years, 1 month ago

Log in to reply

$\lfloor{\frac {5}{4}}\rfloor$ or $\lceil{\frac {4}{5}}\rceil$

- 6 years, 11 months ago

Log in to reply

In a similar way, $\lfloor \sqrt[5]{4} \rfloor, \lfloor \sqrt[4]{5} \rfloor$ etc will also work.

- 6 years, 11 months ago

Log in to reply

Or $\lfloor{\sqrt{\frac {5}{4}}}\rfloor$ and $\lceil{\sqrt{\frac {4}{5}}}\rceil$

- 6 years, 11 months ago

Log in to reply

Thas possible...greatest integer function..👍

- 6 years, 11 months ago

Log in to reply

5 and 4 are used twice

- 6 years, 10 months ago

Log in to reply

No, they're not. They are used only once in each expression. I have written them separately.

- 6 years, 10 months ago

Log in to reply

It's for Kevin's solution.

- 6 years, 10 months ago

Log in to reply

Same goes for Kevin's solution.

- 6 years, 10 months ago

Log in to reply

Ah yes ty I was misled too -_-

- 6 years, 10 months ago

Log in to reply

LOL :D

- 6 years, 10 months ago

Log in to reply

$5 \oplus 4 = 1$

- 6 years, 11 months ago

Log in to reply

this made my day....ahahahah

- 6 years, 11 months ago

Log in to reply

Whats the sign between 5 and 4???

- 6 years, 11 months ago

Log in to reply

You need to describe the modulo number i.e.$5 \bigoplus_84$ for which an extra 8 is required.

- 6 years, 11 months ago

Log in to reply

It's not modulo, but an XOR operation, :)

- 6 years, 11 months ago

Log in to reply

ohkk.....thats right....superb 👍👍👌

- 6 years, 11 months ago

Log in to reply

$\ln \left({\frac{\exp{(5)}}{\exp{(4)}}}\right)=1$

- 6 years, 10 months ago

Log in to reply

Wow....superb !!Gud one👌👌

This one's right.

Edit it to Ln instead of log...

- 6 years, 10 months ago

Log in to reply

I wrote it ln then changed it to log, thought that in english countries, log refers to the natural logarithm. Anyway I'm editing it again :)

- 6 years, 10 months ago

Log in to reply

Yeah...or else $log_e$ is also used.

However Ln seems better...:)

- 6 years, 10 months ago

Log in to reply

5 mod 4 =1

- 6 years, 11 months ago

Log in to reply

Greatest integer(5/4)

- 6 years, 11 months ago

Log in to reply

Yes..this one is possible.

3 more ways are possible.

- 6 years, 11 months ago

Log in to reply

Signum(5+4), Signum(5×4) Signum(5÷4)

- 6 years, 11 months ago

Log in to reply

sgn function is another way. Avoid the functions which always generate 1 for a constant.

Again,find the other ways...

- 6 years, 11 months ago

Log in to reply

$\gcd(4,5)=1$

$|cis(45°)|=1$

- 6 years, 11 months ago

Log in to reply

yeah....cool solution...gud one ✌👍

- 6 years, 11 months ago

Log in to reply

$\frac{\phi(5)}{4} = 1$

- 6 years, 11 months ago

Log in to reply

On a similar note of numerical functions, $d(4)-d(5)=1$ where $d(n)=$the number of positive divisors of n.

- 6 years, 11 months ago

Log in to reply

yup...another solution..

- 6 years, 11 months ago

Log in to reply

$v_4(5!) = 1$

- 6 years, 11 months ago

Log in to reply

Speechless.......

- 6 years, 11 months ago

Log in to reply

What is $\nu$ function ???

- 6 years, 11 months ago

Log in to reply

Highest power of a prime that divides something.In this case it is not used properly, because 4 is not a prime.

- 6 years, 11 months ago

Log in to reply

I believe the function can still be used... This also works: $v_5(\lceil \sqrt{4!} \,\rceil) = 1.$

- 6 years, 11 months ago

Log in to reply

yes it works...

- 6 years, 11 months ago

Log in to reply

Gcd(5,4)=1 The easiest one

- 6 years, 11 months ago

Log in to reply

signum(45),or anything which invlove 4 and 5(but real)

- 6 years, 11 months ago

Log in to reply

yes...signum function is possible...It is a function which always gives 1 for any constant.

- 6 years, 11 months ago

Log in to reply

- 6 years, 5 months ago

Log in to reply

totient funtion of 5 / 4

- 6 years, 11 months ago

Log in to reply

yeah...its possible

(Totient of 5)/4

- 6 years, 11 months ago

Log in to reply

tan(45)=1

integer(5/4)=1 (we use in C language int(a/b) to get integer quotient)

- 6 years, 11 months ago

Log in to reply

5 modulo 4=1

- 6 years, 11 months ago

Log in to reply

Is this possible 5 + 4i^2

- 6 years, 10 months ago

Log in to reply

This gives 1 but extra 2 cant be used as in i^2.

- 6 years, 10 months ago

Log in to reply

Just write it like this: $5+4i \times i=1$

- 6 years, 10 months ago

Log in to reply

Yeah...now it's possible.. Gud 1👍👍

- 6 years, 10 months ago

Log in to reply

Much bypass though.

- 6 years, 10 months ago

Log in to reply

Even like that is not correct; used the imaginary number $i$ while any number other than $5$ or $4$ cannot be used.

- 6 years, 10 months ago

Log in to reply

$\frac{d(\sigma(\sigma(\sigma(\sigma(\sigma(5))))))}{d(\sigma(\sigma(\sigma(\sigma(\sigma(4))))))} = 1$

- 6 years, 10 months ago

Log in to reply

Lawl is that too much... =="

- 6 years, 10 months ago

Log in to reply

Where $d(n)$ is the number of divisors of n and $\sigma(n)$ is the sum of divisors of n.

- 6 years, 10 months ago

Log in to reply

In programming languages (int)5/4=1

- 6 years, 10 months ago

Log in to reply

(5/4) × (4/5) = 1.25 x 0.8 = 1 QED

- 6 years, 11 months ago

Log in to reply

The condition is you cannot use 5 and 4 more than once.

- 6 years, 11 months ago

Log in to reply

Ah fair enough

- 6 years, 11 months ago

Log in to reply

small omega of 5 / small omega of 4 ( note small omega counts the number of distinct prime factors )

- 6 years, 11 months ago

Log in to reply

The most obvious $gcd(5,4)=1$

Also, $\frac{\varphi(5)}{4}=1$

- 6 years, 11 months ago

Log in to reply

yep..The gcd(5,4) is the most obvious.

- 6 years, 11 months ago

Log in to reply

No offence to maths but 4 = IV and 5 = V in roman numerals. So IV/V = I ( after cancelling V on both sides) = 1

- 6 years, 11 months ago

Log in to reply

5%4

- 6 years, 11 months ago

Log in to reply

gcd (4,5)=1

- 6 years, 11 months ago

Log in to reply

what does ceil and floor mean

- 6 years, 11 months ago

Log in to reply

ceil(4/5),floor(5/4)

- 6 years, 11 months ago

Log in to reply

(1) 5%4

- 6 years, 11 months ago

Log in to reply

5%4 (mod)=1

- 6 years, 11 months ago

Log in to reply

5%4.

- 6 years, 11 months ago

Log in to reply

5%4

- 6 years, 11 months ago

Log in to reply

sum to infinity of i=1 (4*5^-i) //sorry but i don't know how to write the notation

- 6 years, 11 months ago

Log in to reply

$\sum_{i=1}^{\infty}4×5^{-i}$

The expression gives the value 1 but extra 1 and $\infty$ cannot be used.

- 6 years, 11 months ago

Log in to reply

(5+4)/(5+4)

- 6 years, 11 months ago

Log in to reply

you've broken the rules

- 6 years, 10 months ago

Log in to reply

Hi Vinay this discussion is a good food for thought....Next

Try to express 0 to 9 numerals using the digit 3 only. One hint is using factorial may come in handy...

- 6 years, 11 months ago

Log in to reply

Thank you...

Generating 0 to 100 will be more interesting..I think you should post a note on it...

- 6 years, 11 months ago

Log in to reply

Also post its link in this note as a comment...

- 6 years, 11 months ago

Log in to reply

Here, I've created a note for this.

- 6 years, 10 months ago

Log in to reply

1. $\lceil \frac{4}{5} \rceil$

- 6 years, 11 months ago

Log in to reply

tan 45

- 6 years, 11 months ago

Log in to reply

5/4=1

Solution : int a=5,b=4,c; c=a/b; (hence c=1)

- 6 years, 11 months ago

Log in to reply

Ya....and even c=5%4

- 6 years, 11 months ago

Log in to reply

5%4=1

- 6 years, 11 months ago

Log in to reply

5 modulo 4

- 6 years, 11 months ago

Log in to reply

5 = 101 (binary notation) 4 = 100 So. 5 xor 4 = 001

- 6 years, 10 months ago

Log in to reply

Cot45= 1

- 6 years, 10 months ago

Log in to reply

5% 4

- 6 years, 10 months ago

Log in to reply

⌊ln(5.4)⌋

- 6 years, 10 months ago

Log in to reply

Log54 to the base 54

- 6 years, 11 months ago

Log in to reply

5 and 4 can be used only once..

- 6 years, 11 months ago

Log in to reply

(5 xor 4) in binary

- 6 years, 11 months ago

Log in to reply

Yes....This is possible even...gr8

- 6 years, 11 months ago

Log in to reply

5/4 remainder is 1 5mod4 is 1

- 6 years, 11 months ago

Log in to reply

5%4=1...Yes,thats one of the ways that I knew.

- 6 years, 11 months ago

Log in to reply

totient function of 4 x .5

- 6 years, 11 months ago

Log in to reply

here 0.5 is not possible...

- 6 years, 11 months ago

Log in to reply

-(4-5)=1 The mirror effect

- 6 years, 11 months ago

Log in to reply

No minus sign.........

- 6 years, 11 months ago

Log in to reply

5%4 =1 , 5$\oplus$4 = 1, $\lfloor\frac {5}{4} \rfloor$ =1, $\lceil \frac {4}{5} \rceil$ =1 ,

- 6 years, 11 months ago

Log in to reply

5%4 = 1 :P .. The % is the modulus sign.. It gives the remainder of 2 non- floating numbers ! As the remainder for floating numbers is zero always!

- 6 years, 11 months ago

Log in to reply

*5 mod 4 =1; *(5+4) mod 4=1;

- 6 years, 11 months ago

Log in to reply

5 (mod 4) is possible but (5+4)(mod 4) is not possible...only one time 5...

- 6 years, 11 months ago

Log in to reply

oh....kk sry

- 6 years, 11 months ago

Log in to reply

(factorial(5)/factorial(4))/5

- 6 years, 11 months ago

Log in to reply

5-4 floor(5/4) ceiling(5/4) 54/54

- 6 years, 11 months ago

Log in to reply

1= 5!/(5×4!)

- 6 years, 11 months ago

Log in to reply

5 and 4 only once...

- 6 years, 11 months ago

Log in to reply

- 6 years, 11 months ago

Log in to reply

abs(5/4)

- 6 years, 11 months ago

Log in to reply

Why not 5 mod 4 p^2

(Actually p^2 is Piyush Patnaik)

- 6 years, 11 months ago

Log in to reply

floor(ln(5)/ln(4)) and ceil(ln(4)/ln(5)) I hope ln(x), the natural logarithm, is acceptable here.

- 6 years, 11 months ago

Log in to reply

Mod(5,4)

- 6 years, 11 months ago

Log in to reply

(4/5)X(5/4)

- 6 years, 11 months ago

Log in to reply

(5*4)^0 =1

- 6 years, 11 months ago

Log in to reply

0 not allowed and

5 and 4 not allowed twice.

- 6 years, 11 months ago

Log in to reply

Dim x as integer; x=5/4

- 6 years, 11 months ago

Log in to reply

5%4=1 what say guys ?

- 6 years, 11 months ago

Log in to reply

We can use 5 XNOR 4 == 1 101 XNOR 100 == 1 What you say?

- 6 years, 11 months ago

Log in to reply

5 xnor 4 = $\overline{101\bigoplus100} = \overline{001}=110$

But 5 xor 1 = 001.

- 6 years, 11 months ago

Log in to reply

Sorry my fault, It's not a valid solution. Solution should be like, we can not only use 5 and 4? ryte?

- 6 years, 11 months ago

Log in to reply

5 and 4 to be used only once and no other numbers.

- 6 years, 11 months ago

Log in to reply

(cos 5) ^2 + (sin 5) ^2 = 1

- 6 years, 11 months ago

Log in to reply

2 cannot be used.

- 6 years, 11 months ago

Log in to reply

can i use concantenation?

$\frac{(5|4)}{54} = \boxed{1}$

- 6 years, 11 months ago

Log in to reply

You can use concatenations

But two times 5 and 4 not allowed.

- 6 years, 11 months ago

Log in to reply

Using Exclusive OR gate. 5=101(b) 4=100(b) In Ex-OR logic output will high if input level is different. Here after computation output is 001(b) its decimal is 1

- 6 years, 11 months ago

Log in to reply

Write a comment or ask a question... 5!/(5*4!)=1

- 6 years, 11 months ago

Log in to reply

No two times 5

- 6 years, 11 months ago

Log in to reply

5%4 = 1

- 6 years, 11 months ago

Log in to reply

5 \times 4 / 5\times 4

- 6 years, 11 months ago

Log in to reply

5 and 4 can be used only once...

- 6 years, 11 months ago

Log in to reply

5 modules 4 = 1

- 6 years, 11 months ago

Log in to reply

5/4

- 6 years, 11 months ago

Log in to reply

5^{0} \times 4^{0}

- 6 years, 11 months ago

Log in to reply

Good one but you used 0

- 6 years, 10 months ago

Log in to reply

can you please explain the notation....??

- 6 years, 11 months ago

Log in to reply

It is 5 raised to 0 divided by 4 raised to 0

- 6 years, 11 months ago

Log in to reply

ohkk... :)

- 6 years, 11 months ago

Log in to reply

5×4=20.Then 20÷20=1

- 6 years, 10 months ago

Log in to reply

!0

- 6 years, 10 months ago

Log in to reply

The 3 solution i no is Lint of 4/5 Zint of 5/4 Tan45

- 6 years, 10 months ago

Log in to reply

(4-5)^{2}

- 6 years, 10 months ago

Log in to reply

'-' sign should not be used and extra numbers cant be used.

- 6 years, 10 months ago

Log in to reply

Mine is easier 5/4 x 4/5

- 6 years, 10 months ago

Log in to reply

((5×4)/5)/4 or ((4×5)/4)/5. They work

- 6 years, 10 months ago

Log in to reply

(5^2+4^2+4)/45

- 6 years, 10 months ago

Log in to reply

( 5 / 4 ) * ( 4 / 5 ) or ( 5 / 5 ) / (4 / 4) something like this :D

- 6 years, 10 months ago

Log in to reply

Nope...you cant use 5 and 4 two times.

- 6 years, 10 months ago

Log in to reply

Tan(45)=1

- 6 years, 10 months ago

Log in to reply

$y\quad =\quad 54x\\ then\\ { [\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ] }!\\ =1$

- 6 years, 10 months ago

Log in to reply

You cannot use 2...

- 6 years, 4 months ago

Log in to reply

4 mod(5)=1

- 6 years, 9 months ago

Log in to reply

5%4 = 1 ie., 5 modulus of 4 = 1

- 6 years, 7 months ago

Log in to reply

$5\quad mod\quad 4,\quad \left\lfloor \frac { 5 }{ 4 } \right\rfloor ,\quad \left\lceil \frac { 4 }{ 5 } \right\rceil ,\quad round\frac { 5 }{ 4 } ,round\frac { 4 }{ 5 } \\ \frac { \Gamma (5) }{ 4! } ,\quad cot(45deg)$

- 6 years, 5 months ago

Log in to reply

5%4=1or equivalently 5mod4=1

- 6 years, 4 months ago

Log in to reply

$\dfrac{\gamma}{4!}$ =$1$

- 6 years, 4 months ago

Log in to reply

uuhgjjjjk

- 6 years, 3 months ago

Log in to reply

(5/4)*(4/5)

- 6 years, 2 months ago

Log in to reply

$\sin{(4+5)}={\lceil}{0.3955...}{\rceil}={\boxed{1}}$

- 2 years, 9 months ago

Log in to reply

5^4

- 6 years, 11 months ago

Log in to reply

54/54 =1,45/45=1,5%4=1,(5*5)%4!

- 6 years, 11 months ago

Log in to reply

Taking (5+4)- (4+4) = 1

- 6 years, 11 months ago

Log in to reply

[5/4]

- 6 years, 11 months ago

Log in to reply

a^0 = 1

- 6 years, 10 months ago

Log in to reply

Nope....0 not to be used.

- 6 years, 10 months ago

Log in to reply

f\left( x \right)=x\ f(5)-f(4)=1

- 6 years, 10 months ago

Log in to reply

How about .5 repeated plus .4 repeated? Does that break the rule for multiple usages of the digits if the horizontal line notation is used?

- 6 years, 9 months ago

Log in to reply

yep..breaks the rule.

- 6 years, 9 months ago

Log in to reply

(5×4)/(10×2)

- 6 years, 11 months ago

Log in to reply

10 and 2 cant be used.

- 6 years, 10 months ago

Log in to reply

54/54

- 6 years, 11 months ago

Log in to reply

(54)/(54)

- 6 years, 11 months ago

Log in to reply

5 x 4 -19

- 6 years, 11 months ago

Log in to reply

nvm... Can't have a - sign

- 6 years, 11 months ago

Log in to reply

(54)/(54)

- 6 years, 11 months ago

Log in to reply

5^0 times 4^0 = 1

- 6 years, 11 months ago

Log in to reply

Wrong answer 0 can't be used

- 6 years, 11 months ago

Log in to reply

nope...0 cant be used.

- 6 years, 11 months ago

Log in to reply

I'LL BLOW ALL OF YOUR MINDS!!!! |4-5|=1

- 6 years, 10 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...