# 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 ?

## Comments

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TopNewestThe four solutions that i know are:

Tan(45)=15%4=1which is same asremainder when 5÷4where \(\Im\) is imaginary number.\(\text{FIVE in Roman = V;}\) \(\text{FOUR in Roman = IV.So,}\) \[\frac{4}{5}=\frac{IV}{V}=I=1\] – Vinay Sipani · 2 years, 10 months ago

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– Tasmeem Reza · 2 years, 9 months ago

\(5^{\mu(4)}\) is also posible, where \(\mu\) defines the MOBIUS function.Log in to reply

– Vinay Sipani · 2 years, 9 months ago

Yes...thats right👍👍 Good use of MOBIUS functionLog in to reply

– Vamshi Krishna Kandula · 2 years, 9 months ago

even cot(45)=1Log in to reply

– Alamuru Ganesh · 2 years, 9 months ago

even cotan(45)=1Log in to reply

– Vinay Sipani · 2 years, 9 months ago

yup..right.👍👍Log in to reply

– Mehul Arora · 2 years, 3 months ago

5 (mod 4) = 1Log in to reply

– Tasmeem Reza · 2 years, 3 months ago

\(\frac{d}{dx}(x+54)=1\)Log in to reply

– Mehul Arora · 2 years, 5 months ago

5-4=1Log in to reply

– Noor Haadi · 2 years, 9 months ago

Woahh, allawwLog in to reply

Same thing as 5-4 but looks different \(\int _{ 4 }^{ 5 }{ dx } = 1\) Lol. X'D – Vishnuram Leonardodavinci · 2 years, 10 months ago

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– Vinay Sipani · 2 years, 10 months ago

yess....even this is possible👍👍Log in to reply

– Sharky Kesa · 2 years, 10 months ago

Nicely done, didn't see that.Log in to reply

\(\dfrac { Gamma(5) }{ 4! } =1\) – Michael Mendrin · 2 years, 10 months ago

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– Tanya Gupta · 2 years, 10 months ago

Could u explain what the gamma() function's purposeLog in to reply

– Michael Mendrin · 2 years, 10 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.Log in to reply

– Tanya Gupta · 2 years, 9 months ago

Woah!!!...thank you so much!!!Log in to reply

– Vinod Kumar Hv · 2 years, 9 months ago

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

@Michael Mendrin – Harsh Shrivastava · 2 years 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! ??Log in to reply

– Vinay Sipani · 2 years, 10 months ago

yeah...never thought of this...👌👍Log in to reply

– Vishnuram Leonardodavinci · 2 years, 10 months ago

Aw yes. :-)Log in to reply

\(\lfloor{\frac {5}{4}}\rfloor\) or \(\lceil{\frac {4}{5}}\rceil\) – Sharky Kesa · 2 years, 10 months ago

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– Chung Kevin · 2 years, 10 months ago

In a similar way, \( \lfloor \sqrt[5]{4} \rfloor, \lfloor \sqrt[4]{5} \rfloor \) etc will also work.Log in to reply

– Sharky Kesa · 2 years, 10 months ago

Or \(\lfloor{\sqrt{\frac {5}{4}}}\rfloor\) and \(\lceil{\sqrt{\frac {4}{5}}}\rceil\)Log in to reply

– Vinay Sipani · 2 years, 10 months ago

Thas possible...greatest integer function..👍Log in to reply

– Vikrant6 Bhatia · 2 years, 9 months ago

5 and 4 are used twiceLog in to reply

– Sharky Kesa · 2 years, 9 months ago

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

– Joshua Ong · 2 years, 8 months ago

It's for Kevin's solution.Log in to reply

– Sharky Kesa · 2 years, 8 months ago

Same goes for Kevin's solution.Log in to reply

– Joshua Ong · 2 years, 8 months ago

Ah yes ty I was misled too -_-Log in to reply

– Sharky Kesa · 2 years, 8 months ago

LOL :DLog in to reply

\(5 \oplus 4 = 1\) – Ammar Fathin Sabili · 2 years, 10 months ago

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– Vinay Sipani · 2 years, 10 months ago

You need to describe the modulo number i.e.\(5 \bigoplus_84\) for which an extra 8 is required.Log in to reply

– Ammar Fathin Sabili · 2 years, 10 months ago

It's not modulo, but an XOR operation, :)Log in to reply

– Vinay Sipani · 2 years, 10 months ago

ohkk.....thats right....superb 👍👍👌Log in to reply

– Tanya Gupta · 2 years, 10 months ago

Whats the sign between 5 and 4???Log in to reply

– Varshith Reddy · 2 years, 10 months ago

this made my day....ahahahahLog in to reply

\[ \ln \left({\frac{\exp{(5)}}{\exp{(4)}}}\right)=1 \] – Zakaria Sellami · 2 years, 9 months ago

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This one's right.

Edit it to Ln instead of log... – Vinay Sipani · 2 years, 9 months ago

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– Zakaria Sellami · 2 years, 9 months 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 :)Log in to reply

However Ln seems better...:) – Vinay Sipani · 2 years, 9 months ago

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5 mod 4 =1 – Tanya Gupta · 2 years, 10 months ago

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\(v_4(5!) = 1\) – Michael Tang · 2 years, 9 months ago

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– Zi Song Yeoh · 2 years, 9 months ago

Speechless.......Log in to reply

– Vinay Sipani · 2 years, 9 months ago

What is \(\nu\) function ???Log in to reply

– Bogdan Simeonov · 2 years, 9 months ago

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

– Michael Tang · 2 years, 9 months ago

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

– Vinay Sipani · 2 years, 9 months ago

yes it works...Log in to reply

\( \frac{\phi(5)}{4} = 1\) – Tan Li Xuan · 2 years, 9 months ago

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– Xuming Liang · 2 years, 9 months ago

On a similar note of numerical functions, \(d(4)-d(5)=1\) where \(d(n)=\)the number of positive divisors of n.Log in to reply

– Vinay Sipani · 2 years, 9 months ago

yup...another solution..Log in to reply

\(\gcd(4,5)=1\)

\(|cis(45°)|=1\) – Alan Enrique Ontiveros Salazar · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

yeah....cool solution...gud one ✌👍Log in to reply

Greatest integer(5/4) – Kushagra Jaiswal · 2 years, 10 months ago

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3 more ways are possible. – Vinay Sipani · 2 years, 10 months ago

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– Kushagra Jaiswal · 2 years, 10 months ago

Signum(5+4), Signum(5×4) Signum(5÷4)Log in to reply

Again,find the other ways... – Vinay Sipani · 2 years, 10 months ago

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\[\Large\color{red}{\left\lceil\frac{\zeta(5)}{\zeta(4)}\right\rceil}\] – Anastasiya Romanova · 2 years, 4 months ago

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signum(45),or anything which invlove 4 and 5(but real) – Tejasvi Singh · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

yes...signum function is possible...It is a function which always gives 1 for any constant.Log in to reply

Gcd(5,4)=1 The easiest one – Mardokay Mosazghi · 2 years, 9 months ago

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In programming languages (int)5/4=1 – Hari Mohan · 2 years, 8 months ago

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\(\frac{d(\sigma(\sigma(\sigma(\sigma(\sigma(5))))))}{d(\sigma(\sigma(\sigma(\sigma(\sigma(4))))))} = 1\) – Samuraiwarm Tsunayoshi · 2 years, 9 months ago

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– Samuraiwarm Tsunayoshi · 2 years, 9 months ago

Lawl is that too much... =="Log in to reply

– Samuraiwarm Tsunayoshi · 2 years, 9 months ago

Where \(d(n)\) is the number of divisors of n and \(\sigma(n)\) is the sum of divisors of n.Log in to reply

Is this possible 5 + 4i^2 – N C · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

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

– Zakaria Sellami · 2 years, 9 months ago

Just write it like this: \(5+4i \times i=1 \)Log in to reply

– Joshua Ong · 2 years, 8 months ago

Much bypass though.Log in to reply

– Zakaria Sellami · 2 years, 8 months ago

Even like that is not correct; used the imaginary number \( i \) while any number other than \(5\) or \(4\) cannot be used.Log in to reply

– Vinay Sipani · 2 years, 9 months ago

Yeah...now it's possible.. Gud 1👍👍Log in to reply

5 modulo 4=1 – Basant K Jha · 2 years, 9 months ago

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tan(45)=1

integer(5/4)=1 (we use in C language int(a/b) to get integer quotient) – Surendra Singh · 2 years, 10 months ago

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totient funtion of 5 / 4 – Alamuru Ganesh · 2 years, 10 months ago

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(Totient of 5)/4 – Vinay Sipani · 2 years, 9 months ago

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5% 4 – Saneel Velangkar · 2 years, 8 months ago

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Cot45= 1 – Husain Kennedy · 2 years, 9 months ago

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5 = 101 (binary notation) 4 = 100 So. 5 xor 4 = 001 – Kunal Krishna · 2 years, 9 months ago

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5 modulo 4 – Debarati Biswas · 2 years, 9 months ago

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5%4=1 – G C Keerthi Vasan · 2 years, 9 months ago

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5/4=1

Solution : int a=5,b=4,c; c=a/b; (hence c=1) – Weerdhaval Chowgule · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

Ya....and even c=5%4Log in to reply

tan 45 – Rohan Lad · 2 years, 9 months ago

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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... – Deepak Gowda · 2 years, 9 months ago

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Generating 0 to 100 will be more interesting..I think you should post a note on it... – Vinay Sipani · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

Also post its link in this note as a comment...Log in to reply

Here, I've created a note for this. – Kenny Lau · 2 years, 8 months ago

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(5+4)/(5+4) – John Errol Obia · 2 years, 9 months ago

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– Priyesh Pandey · 2 years, 9 months ago

you've broken the rulesLog in to reply

sum to infinity of i=1 (4*5^-i) //sorry but i don't know how to write the notation – Youssef Hafez · 2 years, 9 months ago

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The expression gives the value 1 but extra

1 and \(\infty\) cannot be used.– Vinay Sipani · 2 years, 9 months agoLog in to reply

5%4 – Ishan Dixit · 2 years, 9 months ago

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5%4. – Mohit Gupta · 2 years, 9 months ago

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5%4 (mod)=1 – Dushyant Vyas · 2 years, 9 months ago

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(1) 5%4 – Manoj Patial · 2 years, 9 months ago

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ceil(4/5),floor(5/4) – Sushant Ranade · 2 years, 9 months ago

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gcd (4,5)=1 – Sunitha Bhadragiri · 2 years, 9 months ago

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– Kaivalya Swami · 2 years, 9 months ago

what does ceil and floor meanLog in to reply

5%4 – Jude D'silva · 2 years, 9 months ago

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No offence to maths but 4 = IV and 5 = V in roman numerals. So IV/V = I ( after cancelling V on both sides) = 1 – Utkarsh Dwivedi · 2 years, 9 months ago

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

Also, \(\frac{\varphi(5)}{4}=1\) – Bogdan Simeonov · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

yep..The gcd(5,4) is the most obvious.Log in to reply

small omega of 5 / small omega of 4 ( note small omega counts the number of distinct prime factors ) – Alamuru Ganesh · 2 years, 10 months ago

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(5/4) × (4/5) = 1.25 x 0.8 = 1 QED – M Bilal Giga · 2 years, 10 months ago

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– Vinay Sipani · 2 years, 10 months ago

The condition is you cannot use 5 and 4 more than once.Log in to reply

– M Bilal Giga · 2 years, 10 months ago

Ah fair enoughLog in to reply

(5/4)*(4/5) – Irisae Jade · 2 years ago

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uuhgjjjjk – Tergel Myagmarsaikhan · 2 years, 1 month ago

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\(\dfrac{\gamma}{4!}\) =\(1\) – Parth Lohomi · 2 years, 2 months ago

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5%4=1or equivalently 5mod4=1 – Priyesh Pandey · 2 years, 3 months ago

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\(5\quad mod\quad 4,\quad \left\lfloor \frac { 5 }{ 4 } \right\rfloor ,\quad \left\lceil \frac { 4 }{ 5 } \right\rceil ,\quad round\frac { 5 }{ 4 } ,round\frac { 4 }{ 5 } \\ \frac { \Gamma (5) }{ 4! } ,\quad cot(45deg)\) – Archit Boobna · 2 years, 3 months ago

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5%4 = 1 ie., 5 modulus of 4 = 1 – Vasanthakumar Chandrasekaran · 2 years, 6 months ago

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4 mod(5)=1 – Dinesh C · 2 years, 8 months ago

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\(y\quad =\quad 54x\\ then\\ { [\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ] }!\\ =1\) – Rudresh Tomar · 2 years, 8 months ago

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– Vinay Sipani · 2 years, 3 months ago

You cannot use 2...Log in to reply

⌊ln(5.4)⌋ – Kenny Lau · 2 years, 8 months ago

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Tan(45)=1 – Lina .... · 2 years, 8 months ago

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a^0 = 1 – Vhie Yaa Jesus · 2 years, 8 months ago

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– Vinay Sipani · 2 years, 8 months ago

Nope....0 not to be used.Log in to reply

( 5 / 4 ) * ( 4 / 5 ) or ( 5 / 5 ) / (4 / 4) something like this :D – Mario Medhat · 2 years, 8 months ago

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– Vinay Sipani · 2 years, 8 months ago

Nope...you cant use 5 and 4 two times.Log in to reply

(5^2+4^2+4)/45 – Sanjay Mohan · 2 years, 9 months ago

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((5×4)/5)/4 or ((4×5)/4)/5. They work – Nathan Blanco · 2 years, 9 months ago

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Mine is easier 5/4 x 4/5 – Hafizh Ahsan Permana · 2 years, 9 months ago

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– Devendra Sethia · 2 years, 9 months ago

Sorry, it is supposed to be (5X4) instead of (54)Log in to reply

(4-5)^{2} – Roushan Chandan · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

'-' sign should not be used and extra numbers cant be used.Log in to reply

The 3 solution i no is Lint of 4/5 Zint of 5/4 Tan45 – Shehzada Shehzada · 2 years, 9 months ago

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!0 – Cleiston Rodrigues · 2 years, 9 months ago

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5×4=20.Then 20÷20=1 – Kiran Dhamane · 2 years, 9 months ago

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5^{0} \times 4^{0} – Dhruva Kothari · 2 years, 9 months ago

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– Zakaria Sellami · 2 years, 9 months ago

Good one but you used 0Log in to reply

– Charvi Vitthal · 2 years, 9 months ago

can you please explain the notation....??Log in to reply

– Weerdhaval Chowgule · 2 years, 9 months ago

It is 5 raised to 0 divided by 4 raised to 0Log in to reply

– Charvi Vitthal · 2 years, 9 months ago

ohkk... :)Log in to reply

5/4 – Стэн Марш · 2 years, 9 months ago

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5 modules 4 = 1 – Rajat Sharma · 2 years, 9 months ago

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5 \times 4 / 5\times 4 – Vidul Ap · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

5 and 4 can be used only once...Log in to reply

5%4 = 1 – Ferdose Ashraf · 2 years, 9 months ago

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Write a comment or ask a question... 5!/(5*4!)=1 – Aryan Tomar · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

No two times 5Log 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 – Sajedul Mesuk · 2 years, 9 months ago

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can i use concantenation?

\( \frac{(5|4)}{54} = \boxed{1} \) – Barjuan Davis · 2 years, 9 months ago

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But two times 5 and 4 not allowed. – Vinay Sipani · 2 years, 9 months ago

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(cos 5) ^2 + (sin 5) ^2 = 1 – Deepak Gowda · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

2 cannot be used.Log in to reply

We can use 5 XNOR 4 == 1 101 XNOR 100 == 1 What you say? – Arun Gupta · 2 years, 9 months ago

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But 5 xor 1 = 001. – Vinay Sipani · 2 years, 9 months ago

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– Arun Gupta · 2 years, 9 months ago

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

– Vinay Sipani · 2 years, 9 months ago

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

5%4=1 what say guys ? – Ajit Panada · 2 years, 9 months ago

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Dim x as integer; x=5/4 – Dave Dave · 2 years, 9 months ago

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(5*4)^0 =1 – Brahmam Meka · 2 years, 9 months ago

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5 and 4 not allowed twice. – Vinay Sipani · 2 years, 9 months ago

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(4/5)X(5/4) – Biswajit Mohanty · 2 years, 9 months ago

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Mod(5,4) – Muhammad Riaz · 2 years, 9 months ago

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floor(ln(5)/ln(4)) and ceil(ln(4)/ln(5)) I hope ln(x), the natural logarithm, is acceptable here. – Evan Robinson · 2 years, 9 months ago

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abs(5/4) – Piyush Patnaik · 2 years, 9 months ago

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p^2(Actually p^2 is Piyush Patnaik) – Ashutosh Mahapatra · 2 years, 9 months ago

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5#/4! – Ronq Vader · 2 years, 9 months ago

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1= 5!/(5×4!) – Anshul Shivhare · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

5 and 4 only once...Log in to reply

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

4/54 – Ramasubramaniyan Gunasridharan · 2 years, 9 months agoLog in to reply

(factorial(5)/factorial(4))/5 – M Kashif · 2 years, 9 months ago

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*5 mod 4 =1; *(5+4) mod 4=1; – Sam Indhu · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

5 (mod 4) is possible but (5+4)(mod 4) is not possible...only one time 5...Log in to reply

– Sam Indhu · 2 years, 9 months ago

oh....kk sryLog 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! – Akshay Vishwanath · 2 years, 10 months ago

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5%4 =1 , 5\(\oplus\)4 = 1, \(\lfloor\frac {5}{4} \rfloor\) =1, \(\lceil \frac {4}{5} \rceil\) =1 , – Gaurav Sharma · 2 years, 10 months ago

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-(4-5)=1 The mirror effect – Tran Quan · 2 years, 10 months ago

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– Utkarsh Dwivedi · 2 years, 9 months ago

No minus sign.........Log in to reply

totient function of 4 x .5 – Alamuru Ganesh · 2 years, 10 months ago

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.5 is not possible... – Vinay Sipani · 2 years, 9 months ago0Log in to reply

5/4 remainder is 1 5mod4 is 1 – Arun Sowri · 2 years, 10 months ago

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– Vinay Sipani · 2 years, 10 months ago

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

Log54 to the base 54 – Aman Chaudhary · 2 years, 10 months ago

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– Vinay Sipani · 2 years, 10 months ago

5 and 4 can be used only once..Log in to reply

– Dead Call · 2 years, 10 months ago

(5 xor 4) in binaryLog in to reply

– Vinay Sipani · 2 years, 10 months ago

Yes....This is possible even...gr8Log 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? – Brendan Caseria · 2 years, 7 months ago

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– Vinay Sipani · 2 years, 7 months ago

yep..breaks the rule.Log in to reply

f\left( x \right)=x\ f(5)-f(4)=1 – Shrajan Vetcha · 2 years, 8 months ago

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[5/4] – Shantnu Patlan · 2 years, 9 months ago

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Taking (5+4)- (4+4) = 1 – Ahmad Bashir · 2 years, 9 months ago

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54/54 =1,45/45=1,5%4=1,(5*5)%4! – Radha Krishnan B · 2 years, 9 months ago

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5^4 – Sagar Sharma · 2 years, 9 months ago

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(5

4)/(54) – Vidul Ap · 2 years, 9 months agoLog in to reply

5 x 4 -19 – Elita Zheng · 2 years, 9 months ago

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– Elita Zheng · 2 years, 9 months ago

nvm... Can't have a - signLog in to reply

(5

4)/(54) – Brahmam Meka · 2 years, 9 months agoLog in to reply

54/54 – Kaivalya Swami · 2 years, 9 months ago

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(5×4)/(10×2) – Rohan Chaudhary · 2 years, 9 months ago

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– Vinay Sipani · 2 years, 9 months ago

10 and 2 cant be used.Log in to reply

I'LL BLOW ALL OF YOUR MINDS!!!! |4-5|=1 – Nathan Blanco · 2 years, 8 months ago

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5^0 times 4^0 = 1 – Vicneswaran Vicnes · 2 years, 10 months ago

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– Sampad Kar · 2 years, 10 months ago

Wrong answer 0 can't be usedLog in to reply

– Vinay Sipani · 2 years, 10 months ago

nope...0 cant be used.Log in to reply