# 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
7 years, 2 months ago

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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...

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

- 7 years, 2 months ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

even cotan(45)=1

- 7 years, 2 months ago

yup..right.👍👍

- 7 years, 2 months ago

even cot(45)=1

- 7 years, 1 month ago

5 (mod 4) = 1

- 6 years, 7 months ago

5-4=1

- 6 years, 9 months ago

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

- 6 years, 7 months ago

Woahh, allaww

- 7 years, 1 month ago

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

- 7 years, 2 months ago

yess....even this is possible👍👍

- 7 years, 2 months ago

Nicely done, didn't see that.

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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.

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

Aw yes. :-)

- 7 years, 2 months ago

yeah...never thought of this...👌👍

- 7 years, 2 months ago

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, 4 months ago

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

Thas possible...greatest integer function..👍

- 7 years, 2 months ago

5 and 4 are used twice

- 7 years, 1 month ago

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

- 7 years, 1 month ago

It's for Kevin's solution.

- 7 years ago

Same goes for Kevin's solution.

- 7 years ago

Ah yes ty I was misled too -_-

- 7 years ago

LOL :D

- 7 years ago

$5 \oplus 4 = 1$

- 7 years, 2 months ago

- 7 years, 2 months ago

Whats the sign between 5 and 4???

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

ohkk.....thats right....superb 👍👍👌

- 7 years, 2 months ago

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

- 7 years, 1 month ago

Wow....superb !!Gud one👌👌

This one's right.

Edit it to Ln instead of log...

- 7 years, 1 month ago

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 :)

- 7 years, 1 month ago

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

However Ln seems better...:)

- 7 years, 1 month ago

5 mod 4 =1

- 7 years, 2 months ago

Greatest integer(5/4)

- 7 years, 2 months ago

Yes..this one is possible.

3 more ways are possible.

- 7 years, 2 months ago

Signum(5+4), Signum(5×4) Signum(5÷4)

- 7 years, 2 months ago

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

Again,find the other ways...

- 7 years, 2 months ago

$\gcd(4,5)=1$

$|cis(45°)|=1$

- 7 years, 2 months ago

yeah....cool solution...gud one ✌👍

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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

- 7 years, 1 month ago

yup...another solution..

- 7 years, 2 months ago

$v_4(5!) = 1$

- 7 years, 2 months ago

Speechless.......

- 7 years, 1 month ago

What is $\nu$ function ???

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

yes it works...

- 7 years, 1 month ago

Gcd(5,4)=1 The easiest one

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

- 6 years, 8 months ago

totient funtion of 5 / 4

- 7 years, 2 months ago

yeah...its possible

(Totient of 5)/4

- 7 years, 2 months ago

tan(45)=1

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

- 7 years, 2 months ago

5 modulo 4=1

- 7 years, 1 month ago

Is this possible 5 + 4i^2

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

Yeah...now it's possible.. Gud 1👍👍

- 7 years, 1 month ago

Much bypass though.

- 7 years ago

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

- 7 years ago

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

- 7 years, 1 month ago

Lawl is that too much... =="

- 7 years, 1 month ago

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

- 7 years, 1 month ago

In programming languages (int)5/4=1

- 7 years ago

(5/4) × (4/5) = 1.25 x 0.8 = 1 QED

- 7 years, 2 months ago

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

- 7 years, 2 months ago

Ah fair enough

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

5%4

- 7 years, 1 month ago

gcd (4,5)=1

- 7 years, 1 month ago

what does ceil and floor mean

- 7 years, 1 month ago

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

- 7 years, 1 month ago

(1) 5%4

- 7 years, 1 month ago

5%4 (mod)=1

- 7 years, 1 month ago

5%4.

- 7 years, 1 month ago

5%4

- 7 years, 1 month ago

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

- 7 years, 1 month ago

$\sum_{i=1}^{\infty}4×5^{-i}$

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

- 7 years, 1 month ago

(5+4)/(5+4)

- 7 years, 1 month ago

you've broken the rules

- 7 years, 1 month ago

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...

- 7 years, 1 month ago

Thank you...

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

Here, I've created a note for this.

- 7 years ago

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

- 7 years, 1 month ago

tan 45

- 7 years, 1 month ago

5/4=1

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

5%4=1

- 7 years, 1 month ago

5 modulo 4

- 7 years, 1 month ago

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

- 7 years, 1 month ago

Cot45= 1

- 7 years, 1 month ago

5% 4

- 7 years, 1 month ago

⌊ln(5.4)⌋

- 7 years ago

Log54 to the base 54

- 7 years, 2 months ago

5 and 4 can be used only once..

- 7 years, 2 months ago

(5 xor 4) in binary

- 7 years, 2 months ago

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

- 7 years, 2 months ago

5/4 remainder is 1 5mod4 is 1

- 7 years, 2 months ago

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

- 7 years, 2 months ago

totient function of 4 x .5

- 7 years, 2 months ago

here 0.5 is not possible...

- 7 years, 2 months ago

-(4-5)=1 The mirror effect

- 7 years, 2 months ago

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

- 7 years, 1 month ago

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

- 7 years, 2 months ago

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!

- 7 years, 2 months ago

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

oh....kk sry

- 7 years, 1 month ago

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

- 7 years, 2 months ago

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

- 7 years, 2 months ago

1= 5!/(5×4!)

- 7 years, 2 months ago

5 and 4 only once...

- 7 years, 1 month ago

- 7 years, 1 month ago

abs(5/4)

- 7 years, 1 month ago

Why not 5 mod 4 p^2

(Actually p^2 is Piyush Patnaik)

- 7 years, 1 month ago

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

- 7 years, 1 month ago

Mod(5,4)

- 7 years, 1 month ago

(4/5)X(5/4)

- 7 years, 1 month ago

(5*4)^0 =1

- 7 years, 1 month ago

0 not allowed and

5 and 4 not allowed twice.

- 7 years, 1 month ago

Dim x as integer; x=5/4

- 7 years, 1 month ago

5%4=1 what say guys ?

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

But 5 xor 1 = 001.

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

2 cannot be used.

- 7 years, 1 month ago

can i use concantenation?

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

- 7 years, 1 month ago

You can use concatenations

But two times 5 and 4 not allowed.

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

No two times 5

- 7 years, 1 month ago

5%4 = 1

- 7 years, 1 month ago

5 \times 4 / 5\times 4

- 7 years, 1 month ago

5 and 4 can be used only once...

- 7 years, 1 month ago

5 modules 4 = 1

- 7 years, 1 month ago

5/4

- 7 years, 1 month ago

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

- 7 years, 1 month ago

Good one but you used 0

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

ohkk... :)

- 7 years, 1 month ago

5×4=20.Then 20÷20=1

- 7 years, 1 month ago

!0

- 7 years, 1 month ago

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

- 7 years, 1 month ago

(4-5)^{2}

- 7 years, 1 month ago

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

- 7 years, 1 month ago

Mine is easier 5/4 x 4/5

- 7 years, 1 month ago

((5×4)/5)/4 or ((4×5)/4)/5. They work

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years ago

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

- 7 years ago

Tan(45)=1

- 7 years ago

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

- 7 years ago

You cannot use 2...

- 6 years, 7 months ago

4 mod(5)=1

- 7 years ago

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

- 6 years, 10 months ago

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

- 6 years, 8 months ago

5%4=1or equivalently 5mod4=1

- 6 years, 7 months ago

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

- 6 years, 7 months ago

uuhgjjjjk

- 6 years, 5 months ago

(5/4)*(4/5)

- 6 years, 4 months ago

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

- 3 years ago

5^4

- 7 years, 1 month ago

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

- 7 years, 1 month ago

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

- 7 years, 1 month ago

[5/4]

- 7 years, 1 month ago

a^0 = 1

- 7 years ago

Nope....0 not to be used.

- 7 years ago

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

- 7 years ago

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, 11 months ago

yep..breaks the rule.

- 6 years, 11 months ago

(5×4)/(10×2)

- 7 years, 2 months ago

10 and 2 cant be used.

- 7 years, 1 month ago

54/54

- 7 years, 1 month ago

(54)/(54)

- 7 years, 1 month ago

5 x 4 -19

- 7 years, 1 month ago

nvm... Can't have a - sign

- 7 years, 1 month ago

(54)/(54)

- 7 years, 1 month ago

5^0 times 4^0 = 1

- 7 years, 2 months ago

Wrong answer 0 can't be used

- 7 years, 2 months ago

nope...0 cant be used.

- 7 years, 2 months ago

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

- 7 years ago