5 - 4 = 1 is too easy !!!

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
4 years, 1 month 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...

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

Vinay Sipani - 4 years, 1 month ago

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

Tasmeem Reza - 4 years ago

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

Vinay Sipani - 4 years ago

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even cot(45)=1

Vamshi Krishna Kandula - 4 years, 1 month ago

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even cotan(45)=1

Alamuru Ganesh - 4 years, 1 month ago

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yup..right.👍👍

Vinay Sipani - 4 years, 1 month ago

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5 (mod 4) = 1

Mehul Arora - 3 years, 6 months ago

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

Tasmeem Reza - 3 years, 6 months ago

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5-4=1

Mehul Arora - 3 years, 8 months ago

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Woahh, allaww

Noor Haadi - 4 years, 1 month ago

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

Vishnuram Leonardodavinci - 4 years, 1 month ago

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yess....even this is possible👍👍

Vinay Sipani - 4 years, 1 month ago

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Nicely done, didn't see that.

Sharky Kesa - 4 years, 1 month ago

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

Michael Mendrin - 4 years, 1 month ago

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

Tanya Gupta - 4 years, 1 month ago

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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.

Michael Mendrin - 4 years, 1 month ago

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@Michael Mendrin Woah!!!...thank you so much!!!

Tanya Gupta - 4 years, 1 month ago

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

Vinod Kumar Hv - 4 years, 1 month ago

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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

Harsh Shrivastava - 3 years, 4 months ago

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yeah...never thought of this...👌👍

Vinay Sipani - 4 years, 1 month ago

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Aw yes. :-)

Vishnuram Leonardodavinci - 4 years, 1 month ago

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\(\lfloor{\frac {5}{4}}\rfloor\) or \(\lceil{\frac {4}{5}}\rceil\)

Sharky Kesa - 4 years, 1 month ago

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

Chung Kevin - 4 years, 1 month ago

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

Sharky Kesa - 4 years, 1 month ago

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Thas possible...greatest integer function..👍

Vinay Sipani - 4 years, 1 month ago

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5 and 4 are used twice

Vikrant6 Bhatia - 4 years ago

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

Sharky Kesa - 4 years ago

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@Sharky Kesa It's for Kevin's solution.

Joshua Ong - 4 years ago

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@Joshua Ong Same goes for Kevin's solution.

Sharky Kesa - 4 years ago

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@Sharky Kesa Ah yes ty I was misled too -_-

Joshua Ong - 4 years ago

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@Joshua Ong LOL :D

Sharky Kesa - 4 years ago

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\(5 \oplus 4 = 1\)

Ammar Fathin Sabili - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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

Ammar Fathin Sabili - 4 years, 1 month ago

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@Ammar Fathin Sabili ohkk.....thats right....superb 👍👍👌

Vinay Sipani - 4 years, 1 month ago

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Whats the sign between 5 and 4???

Tanya Gupta - 4 years, 1 month ago

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this made my day....ahahahah

Varshith Reddy - 4 years, 1 month ago

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

Zakaria Sellami - 4 years, 1 month ago

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Wow....superb !!Gud one👌👌

This one's right.

Edit it to Ln instead of log...

Vinay Sipani - 4 years, 1 month ago

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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 :)

Zakaria Sellami - 4 years, 1 month ago

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@Zakaria Sellami Yeah...or else \(log_e\) is also used.

However Ln seems better...:)

Vinay Sipani - 4 years, 1 month ago

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5 mod 4 =1

Tanya Gupta - 4 years, 1 month ago

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\(v_4(5!) = 1\)

Michael Tang - 4 years, 1 month ago

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Speechless.......

Zi Song Yeoh - 4 years, 1 month ago

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What is \(\nu\) function ???

Vinay Sipani - 4 years, 1 month ago

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

Bogdan Simeonov - 4 years, 1 month ago

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

Michael Tang - 4 years, 1 month ago

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@Michael Tang yes it works...

Vinay Sipani - 4 years, 1 month ago

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

Tan Li Xuan - 4 years, 1 month ago

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

Xuming Liang - 4 years, 1 month ago

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yup...another solution..

Vinay Sipani - 4 years, 1 month ago

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

\(|cis(45°)|=1\)

Alan Enrique Ontiveros Salazar - 4 years, 1 month ago

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yeah....cool solution...gud one ✌👍

Vinay Sipani - 4 years, 1 month ago

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Greatest integer(5/4)

Kushagra Jaiswal - 4 years, 1 month ago

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Yes..this one is possible.

3 more ways are possible.

Vinay Sipani - 4 years, 1 month ago

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Signum(5+4), Signum(5×4) Signum(5÷4)

Kushagra Jaiswal - 4 years, 1 month ago

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

Again,find the other ways...

Vinay Sipani - 4 years, 1 month ago

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

Tejasvi Singh - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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Gcd(5,4)=1 The easiest one

Mardokay Mosazghi - 4 years, 1 month ago

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In programming languages (int)5/4=1

Hari Mohan - 4 years ago

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

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Lawl is that too much... =="

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

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Is this possible 5 + 4i^2

N C - 4 years ago

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

Vinay Sipani - 4 years ago

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

Zakaria Sellami - 4 years ago

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@Zakaria Sellami Much bypass though.

Joshua Ong - 4 years ago

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@Joshua Ong Even like that is not correct; used the imaginary number \( i \) while any number other than \(5\) or \(4\) cannot be used.

Zakaria Sellami - 4 years ago

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@Zakaria Sellami Yeah...now it's possible.. Gud 1👍👍

Vinay Sipani - 4 years ago

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5 modulo 4=1

Basant K Jha - 4 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 - 4 years, 1 month ago

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totient funtion of 5 / 4

Alamuru Ganesh - 4 years, 1 month ago

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yeah...its possible

(Totient of 5)/4

Vinay Sipani - 4 years, 1 month ago

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⌊ln(5.4)⌋

Kenny Lau - 4 years ago

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5% 4

Saneel Velangkar - 4 years ago

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Cot45= 1

Husain Kennedy - 4 years ago

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

Kunal Krishna - 4 years ago

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5 modulo 4

Debarati Biswas - 4 years, 1 month ago

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5%4=1

G C Keerthi Vasan - 4 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 - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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tan 45

Rohan Lad - 4 years, 1 month ago

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  1. \(\lceil \frac{4}{5} \rceil\)

Happy Melodies - 4 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 - 4 years, 1 month ago

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Thank you...

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

Vinay Sipani - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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Here, I've created a note for this.

Kenny Lau - 4 years ago

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(5+4)/(5+4)

John Errol Obia - 4 years, 1 month ago

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you've broken the rules

Priyesh Pandey - 4 years ago

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

Youssef Hafez - 4 years, 1 month ago

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\(\sum_{i=1}^{\infty}4×5^{-i}\)

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

Vinay Sipani - 4 years, 1 month ago

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5%4

Ishan Dixit - 4 years, 1 month ago

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5%4.

Mohit Gupta - 4 years, 1 month ago

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5%4 (mod)=1

Dushyant Vyas - 4 years, 1 month ago

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(1) 5%4

Manoj Patial - 4 years, 1 month ago

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

Sushant Ranade - 4 years, 1 month ago

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gcd (4,5)=1

Sunitha Bhadragiri - 4 years, 1 month ago

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what does ceil and floor mean

Kaivalya Swami - 4 years, 1 month ago

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5%4

Jude D'silva - 4 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 - 4 years, 1 month ago

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

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

Bogdan Simeonov - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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

Alamuru Ganesh - 4 years, 1 month ago

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(5/4) × (4/5) = 1.25 x 0.8 = 1 QED

M Bilal Giga - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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Ah fair enough

M Bilal Giga - 4 years, 1 month ago

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(5/4)*(4/5)

Irisae Jade - 3 years, 4 months ago

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uuhgjjjjk

Tergel Myagmarsaikhan - 3 years, 5 months ago

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\(\dfrac{\gamma}{4!}\) =\(1\)

Parth Lohomi - 3 years, 6 months ago

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5%4=1or equivalently 5mod4=1

Priyesh Pandey - 3 years, 6 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 - 3 years, 7 months ago

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

Vasanthakumar Chandrasekaran - 3 years, 10 months ago

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4 mod(5)=1

Dinesh C - 3 years, 11 months ago

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

Rudresh Tomar - 4 years ago

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You cannot use 2...

Vinay Sipani - 3 years, 6 months ago

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Tan(45)=1

Lina .... - 4 years ago

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

Mario Medhat - 4 years ago

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

Vinay Sipani - 4 years ago

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

Sanjay Mohan - 4 years ago

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((5×4)/5)/4 or ((4×5)/4)/5. They work

Nathan Blanco - 4 years ago

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Mine is easier 5/4 x 4/5

Hafizh Ahsan Permana - 4 years ago

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Comment deleted Jun 29, 2014

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

Devendra Sethia - 4 years ago

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(4-5)^{2}

Brilliant Member - 4 years ago

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

Vinay Sipani - 4 years ago

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

Shehzada Shehzada - 4 years ago

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!0

Cleiston Rodrigues - 4 years ago

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5×4=20.Then 20÷20=1

Kiran Dhamane - 4 years, 1 month ago

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

Dhruva Kothari - 4 years, 1 month ago

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Good one but you used 0

Zakaria Sellami - 4 years, 1 month ago

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

Charvi Vitthal - 4 years, 1 month ago

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

Weerdhaval Chowgule - 4 years, 1 month ago

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@Weerdhaval Chowgule ohkk... :)

Charvi Vitthal - 4 years, 1 month ago

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5/4

Стэн Марш - 4 years, 1 month ago

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5 modules 4 = 1

Rajat Sharma - 4 years, 1 month ago

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5 \times 4 / 5\times 4

Vidul Ap - 4 years, 1 month ago

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5 and 4 can be used only once...

Vinay Sipani - 4 years, 1 month ago

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5%4 = 1

Ferdose Ashraf - 4 years, 1 month ago

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

Aryan Tomar - 4 years, 1 month ago

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No two times 5

Vinay Sipani - 4 years, 1 month ago

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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 - 4 years, 1 month ago

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can i use concantenation?

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

Barjuan Davis - 4 years, 1 month ago

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You can use concatenations

But two times 5 and 4 not allowed.

Vinay Sipani - 4 years, 1 month ago

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

Deepak Gowda - 4 years, 1 month ago

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2 cannot be used.

Vinay Sipani - 4 years, 1 month ago

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

Arun Gupta - 4 years, 1 month ago

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

But 5 xor 1 = 001.

Vinay Sipani - 4 years, 1 month ago

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

Arun Gupta - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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5%4=1 what say guys ?

Ajit Panada - 4 years, 1 month ago

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Dim x as integer; x=5/4

Dave Dave - 4 years, 1 month ago

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(5*4)^0 =1

Brahmam Meka - 4 years, 1 month ago

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0 not allowed and

5 and 4 not allowed twice.

Vinay Sipani - 4 years, 1 month ago

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(4/5)X(5/4)

Biswajit Mohanty - 4 years, 1 month ago

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Mod(5,4)

Muhammad Riaz - 4 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 - 4 years, 1 month ago

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abs(5/4)

Piyush Patnaik - 4 years, 1 month ago

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Why not 5 mod 4 p^2

(Actually p^2 is Piyush Patnaik)

Ashutosh Mahapatra - 4 years, 1 month ago

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5#/4!

Ronq Vader - 4 years, 1 month ago

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1= 5!/(5×4!)

Anshul Shivhare - 4 years, 1 month ago

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5 and 4 only once...

Vinay Sipani - 4 years, 1 month ago

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

Ramasubramaniyan Gunasridharan - 4 years, 1 month ago

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

M Kashif - 4 years, 1 month ago

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

Sam Indhu - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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oh....kk sry

Sam Indhu - 4 years, 1 month ago

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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 - 4 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 - 4 years, 1 month ago

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-(4-5)=1 The mirror effect

Tran Quan - 4 years, 1 month ago

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

Utkarsh Dwivedi - 4 years, 1 month ago

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totient function of 4 x .5

Alamuru Ganesh - 4 years, 1 month ago

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here 0.5 is not possible...

Vinay Sipani - 4 years, 1 month ago

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5/4 remainder is 1 5mod4 is 1

Arun Sowri - 4 years, 1 month ago

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

Vinay Sipani - 4 years, 1 month ago

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Log54 to the base 54

Aman Chaudhary - 4 years, 1 month ago

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5 and 4 can be used only once..

Vinay Sipani - 4 years, 1 month ago

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(5 xor 4) in binary

Dead Call - 4 years, 1 month ago

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@Dead Call Yes....This is possible even...gr8

Vinay Sipani - 4 years, 1 month ago

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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 - 3 years, 11 months ago

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yep..breaks the rule.

Vinay Sipani - 3 years, 11 months ago

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

Shrajan Vetcha - 4 years ago

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a^0 = 1

Vhie Yaa Jesus - 4 years ago

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Nope....0 not to be used.

Vinay Sipani - 4 years ago

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[5/4]

Shantnu Patlan - 4 years, 1 month ago

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

Ahmad Bashir - 4 years, 1 month ago

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

Radha Krishnan B - 4 years, 1 month ago

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5^4

Sagar Sharma - 4 years, 1 month ago

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(54)/(54)

Vidul Ap - 4 years, 1 month ago

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5 x 4 -19

Elita Zheng - 4 years, 1 month ago

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nvm... Can't have a - sign

Elita Zheng - 4 years, 1 month ago

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(54)/(54)

Brahmam Meka - 4 years, 1 month ago

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54/54

Kaivalya Swami - 4 years, 1 month ago

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(5×4)/(10×2)

Rohan Chaudhary - 4 years, 1 month ago

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10 and 2 cant be used.

Vinay Sipani - 4 years ago

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

Nathan Blanco - 4 years ago

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5^0 times 4^0 = 1

Vicneswaran Vicnes - 4 years, 1 month ago

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Wrong answer 0 can't be used

Sampad Kar - 4 years, 1 month ago

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nope...0 cant be used.

Vinay Sipani - 4 years, 1 month ago

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