# 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 · 3 years, 1 month ago

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– Tasmeem Reza · 3 years, 1 month ago

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

– Vinay Sipani · 3 years ago

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

– Vamshi Krishna Kandula · 3 years, 1 month ago

even cot(45)=1Log in to reply

– Alamuru Ganesh · 3 years, 1 month ago

even cotan(45)=1Log in to reply

– Vinay Sipani · 3 years, 1 month ago

yup..right.👍👍Log in to reply

– Mehul Arora · 2 years, 7 months ago

5 (mod 4) = 1Log in to reply

– Tasmeem Reza · 2 years, 7 months ago

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

– Mehul Arora · 2 years, 9 months ago

5-4=1Log in to reply

– Noor Haadi · 3 years, 1 month ago

Woahh, allawwLog in to reply

Same thing as 5-4 but looks different \(\int _{ 4 }^{ 5 }{ dx } = 1\) Lol. X'D – Vishnuram Leonardodavinci · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month ago

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

– Sharky Kesa · 3 years, 1 month ago

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

\(\dfrac { Gamma(5) }{ 4! } =1\) – Michael Mendrin · 3 years, 1 month ago

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– Tanya Gupta · 3 years, 1 month ago

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

– Michael Mendrin · 3 years, 1 month 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 · 3 years, 1 month ago

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

– Vinod Kumar Hv · 3 years, 1 month 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, 4 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! ??Log in to reply

– Vinay Sipani · 3 years, 1 month ago

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

– Vishnuram Leonardodavinci · 3 years, 1 month ago

Aw yes. :-)Log in to reply

\(\lfloor{\frac {5}{4}}\rfloor\) or \(\lceil{\frac {4}{5}}\rceil\) – Sharky Kesa · 3 years, 1 month ago

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– Chung Kevin · 3 years, 1 month 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 · 3 years, 1 month ago

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

– Vinay Sipani · 3 years, 1 month ago

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

– Vikrant6 Bhatia · 3 years, 1 month ago

5 and 4 are used twiceLog in to reply

– Sharky Kesa · 3 years, 1 month ago

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

– Joshua Ong · 3 years ago

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

– Sharky Kesa · 3 years ago

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

– Joshua Ong · 3 years ago

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

– Sharky Kesa · 3 years ago

LOL :DLog in to reply

\(5 \oplus 4 = 1\) – Ammar Fathin Sabili · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month 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 · 3 years, 1 month ago

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

– Vinay Sipani · 3 years, 1 month ago

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

– Tanya Gupta · 3 years, 1 month ago

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

– Varshith Reddy · 3 years, 1 month ago

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

\[ \ln \left({\frac{\exp{(5)}}{\exp{(4)}}}\right)=1 \] – Zakaria Sellami · 3 years, 1 month ago

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This one's right.

Edit it to Ln instead of log... – Vinay Sipani · 3 years, 1 month ago

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– Zakaria Sellami · 3 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 :)Log in to reply

However Ln seems better...:) – Vinay Sipani · 3 years, 1 month ago

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5 mod 4 =1 – Tanya Gupta · 3 years, 1 month ago

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\(v_4(5!) = 1\) – Michael Tang · 3 years, 1 month ago

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– Zi Song Yeoh · 3 years, 1 month ago

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

– Vinay Sipani · 3 years, 1 month ago

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

– Bogdan Simeonov · 3 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.Log in to reply

– Michael Tang · 3 years, 1 month 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 · 3 years, 1 month ago

yes it works...Log in to reply

\( \frac{\phi(5)}{4} = 1\) – Tan Li Xuan · 3 years, 1 month ago

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– Xuming Liang · 3 years, 1 month 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 · 3 years, 1 month ago

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

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

\(|cis(45°)|=1\) – Alan Enrique Ontiveros Salazar · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month ago

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

Greatest integer(5/4) – Kushagra Jaiswal · 3 years, 2 months ago

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

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– Kushagra Jaiswal · 3 years, 2 months ago

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

Again,find the other ways... – Vinay Sipani · 3 years, 2 months ago

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\[\Large\color{red}{\left\lceil\frac{\zeta(5)}{\zeta(4)}\right\rceil}\] – Anastasiya Romanova · 2 years, 8 months ago

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signum(45),or anything which invlove 4 and 5(but real) – Tejasvi Singh · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month 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 · 3 years, 1 month ago

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In programming languages (int)5/4=1 – Hari Mohan · 3 years ago

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\(\frac{d(\sigma(\sigma(\sigma(\sigma(\sigma(5))))))}{d(\sigma(\sigma(\sigma(\sigma(\sigma(4))))))} = 1\) – Samuraiwarm Tsunayoshi · 3 years ago

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– Samuraiwarm Tsunayoshi · 3 years ago

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

– Samuraiwarm Tsunayoshi · 3 years 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 · 3 years ago

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– Vinay Sipani · 3 years ago

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

– Zakaria Sellami · 3 years ago

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

– Joshua Ong · 3 years ago

Much bypass though.Log in to reply

– Zakaria Sellami · 3 years 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 · 3 years ago

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

5 modulo 4=1 – Basant K Jha · 3 years, 1 month 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 · 3 years, 1 month ago

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totient funtion of 5 / 4 – Alamuru Ganesh · 3 years, 1 month ago

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(Totient of 5)/4 – Vinay Sipani · 3 years, 1 month ago

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5% 4 – Saneel Velangkar · 3 years ago

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Cot45= 1 – Husain Kennedy · 3 years, 1 month ago

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5 = 101 (binary notation) 4 = 100 So. 5 xor 4 = 001 – Kunal Krishna · 3 years, 1 month ago

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5 modulo 4 – Debarati Biswas · 3 years, 1 month ago

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5%4=1 – G C Keerthi Vasan · 3 years, 1 month ago

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5/4=1

Solution : int a=5,b=4,c; c=a/b; (hence c=1) – Weerdhaval Chowgule · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month ago

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

tan 45 – Rohan Lad · 3 years, 1 month 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 · 3 years, 1 month ago

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Generating 0 to 100 will be more interesting..I think you should post a note on it... – Vinay Sipani · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month 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 · 3 years ago

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(5+4)/(5+4) – John Errol Obia · 3 years, 1 month ago

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– Priyesh Pandey · 3 years 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 · 3 years, 1 month ago

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The expression gives the value 1 but extra

1 and \(\infty\) cannot be used.– Vinay Sipani · 3 years, 1 month agoLog in to reply

5%4 – Ishan Dixit · 3 years, 1 month ago

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5%4. – Mohit Gupta · 3 years, 1 month ago

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5%4 (mod)=1 – Dushyant Vyas · 3 years, 1 month ago

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(1) 5%4 – Manoj Patial · 3 years, 1 month ago

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ceil(4/5),floor(5/4) – Sushant Ranade · 3 years, 1 month ago

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gcd (4,5)=1 – Sunitha Bhadragiri · 3 years, 1 month ago

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– Kaivalya Swami · 3 years, 1 month ago

what does ceil and floor meanLog in to reply

5%4 – Jude D'silva · 3 years, 1 month 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 · 3 years, 1 month ago

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

Also, \(\frac{\varphi(5)}{4}=1\) – Bogdan Simeonov · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month 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 · 3 years, 1 month ago

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(5/4) × (4/5) = 1.25 x 0.8 = 1 QED – M Bilal Giga · 3 years, 2 months ago

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– Vinay Sipani · 3 years, 2 months ago

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

– M Bilal Giga · 3 years, 2 months ago

Ah fair enoughLog in to reply

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

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uuhgjjjjk – Tergel Myagmarsaikhan · 2 years, 5 months ago

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\(\dfrac{\gamma}{4!}\) =\(1\) – Parth Lohomi · 2 years, 7 months ago

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5%4=1or equivalently 5mod4=1 – Priyesh Pandey · 2 years, 7 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, 7 months ago

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5%4 = 1 ie., 5 modulus of 4 = 1 – Vasanthakumar Chandrasekaran · 2 years, 10 months ago

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4 mod(5)=1 – Dinesh C · 2 years, 12 months ago

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\(y\quad =\quad 54x\\ then\\ { [\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ] }!\\ =1\) – Rudresh Tomar · 3 years ago

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– Vinay Sipani · 2 years, 7 months ago

You cannot use 2...Log in to reply

⌊ln(5.4)⌋ – Kenny Lau · 3 years ago

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Tan(45)=1 – Lina .... · 3 years ago

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a^0 = 1 – Vhie Yaa Jesus · 3 years ago

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– Vinay Sipani · 3 years 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 · 3 years ago

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– Vinay Sipani · 3 years ago

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

(5^2+4^2+4)/45 – Sanjay Mohan · 3 years ago

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((5×4)/5)/4 or ((4×5)/4)/5. They work – Nathan Blanco · 3 years ago

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Mine is easier 5/4 x 4/5 – Hafizh Ahsan Permana · 3 years ago

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– Devendra Sethia · 3 years ago

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

(4-5)^{2} – Brilliant Member · 3 years ago

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– Vinay Sipani · 3 years 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 · 3 years, 1 month ago

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!0 – Cleiston Rodrigues · 3 years, 1 month ago

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5×4=20.Then 20÷20=1 – Kiran Dhamane · 3 years, 1 month ago

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5^{0} \times 4^{0} – Dhruva Kothari · 3 years, 1 month ago

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– Zakaria Sellami · 3 years, 1 month ago

Good one but you used 0Log in to reply

– Charvi Vitthal · 3 years, 1 month ago

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

– Weerdhaval Chowgule · 3 years, 1 month ago

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

– Charvi Vitthal · 3 years, 1 month ago

ohkk... :)Log in to reply

5/4 – Стэн Марш · 3 years, 1 month ago

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5 modules 4 = 1 – Rajat Sharma · 3 years, 1 month ago

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5 \times 4 / 5\times 4 – Vidul Ap · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month ago

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

5%4 = 1 – Ferdose Ashraf · 3 years, 1 month ago

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Write a comment or ask a question... 5!/(5*4!)=1 – Aryan Tomar · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month 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 · 3 years, 1 month ago

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can i use concantenation?

\( \frac{(5|4)}{54} = \boxed{1} \) – Barjuan Davis · 3 years, 1 month ago

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But two times 5 and 4 not allowed. – Vinay Sipani · 3 years, 1 month ago

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(cos 5) ^2 + (sin 5) ^2 = 1 – Deepak Gowda · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month 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 · 3 years, 1 month ago

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But 5 xor 1 = 001. – Vinay Sipani · 3 years, 1 month ago

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– Arun Gupta · 3 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?Log in to reply

– Vinay Sipani · 3 years, 1 month 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 · 3 years, 1 month ago

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Dim x as integer; x=5/4 – Dave Dave · 3 years, 1 month ago

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(5*4)^0 =1 – Brahmam Meka · 3 years, 1 month ago

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5 and 4 not allowed twice. – Vinay Sipani · 3 years, 1 month ago

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(4/5)X(5/4) – Biswajit Mohanty · 3 years, 1 month ago

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Mod(5,4) – Muhammad Riaz · 3 years, 1 month 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 · 3 years, 1 month ago

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abs(5/4) – Piyush Patnaik · 3 years, 1 month ago

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p^2(Actually p^2 is Piyush Patnaik) – Ashutosh Mahapatra · 3 years, 1 month ago

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5#/4! – Ronq Vader · 3 years, 1 month ago

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1= 5!/(5×4!) – Anshul Shivhare · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month ago

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

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

4/54 – Ramasubramaniyan Gunasridharan · 3 years, 1 month agoLog in to reply

(factorial(5)/factorial(4))/5 – M Kashif · 3 years, 1 month ago

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*5 mod 4 =1; *(5+4) mod 4=1; – Sam Indhu · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month ago

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

– Sam Indhu · 3 years, 1 month 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 · 3 years, 1 month 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 · 3 years, 1 month ago

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-(4-5)=1 The mirror effect – Tran Quan · 3 years, 1 month ago

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– Utkarsh Dwivedi · 3 years, 1 month ago

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

totient function of 4 x .5 – Alamuru Ganesh · 3 years, 1 month ago

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.5 is not possible... – Vinay Sipani · 3 years, 1 month ago0Log in to reply

5/4 remainder is 1 5mod4 is 1 – Arun Sowri · 3 years, 1 month ago

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– Vinay Sipani · 3 years, 1 month ago

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

Log54 to the base 54 – Aman Chaudhary · 3 years, 2 months ago

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– Vinay Sipani · 3 years, 2 months ago

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

– Dead Call · 3 years, 1 month ago

(5 xor 4) in binaryLog in to reply

– Vinay Sipani · 3 years, 1 month 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, 11 months ago

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– Vinay Sipani · 2 years, 11 months ago

yep..breaks the rule.Log in to reply

f\left( x \right)=x\ f(5)-f(4)=1 – Shrajan Vetcha · 3 years ago

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[5/4] – Shantnu Patlan · 3 years, 1 month ago

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Taking (5+4)- (4+4) = 1 – Ahmad Bashir · 3 years, 1 month ago

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54/54 =1,45/45=1,5%4=1,(5*5)%4! – Radha Krishnan B · 3 years, 1 month ago

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5^4 – Sagar Sharma · 3 years, 1 month ago

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(5

4)/(54) – Vidul Ap · 3 years, 1 month agoLog in to reply

5 x 4 -19 – Elita Zheng · 3 years, 1 month ago

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– Elita Zheng · 3 years, 1 month ago

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

(5

4)/(54) – Brahmam Meka · 3 years, 1 month agoLog in to reply

54/54 – Kaivalya Swami · 3 years, 1 month ago

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(5×4)/(10×2) – Rohan Chaudhary · 3 years, 1 month ago

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– Vinay Sipani · 3 years ago

10 and 2 cant be used.Log in to reply

I'LL BLOW ALL OF YOUR MINDS!!!! |4-5|=1 – Nathan Blanco · 3 years ago

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5^0 times 4^0 = 1 – Vicneswaran Vicnes · 3 years, 1 month ago

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– Sampad Kar · 3 years, 1 month ago

Wrong answer 0 can't be usedLog in to reply

– Vinay Sipani · 3 years, 1 month ago

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