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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
2 years, 8 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...

\(\text{FIVE in Roman = V;}\) \(\text{FOUR in Roman = IV.So,}\) \[\frac{4}{5}=\frac{IV}{V}=I=1\] Vinay Sipani · 2 years, 7 months ago

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@Vinay Sipani \(5^{\mu(4)}\) is also posible, where \(\mu\) defines the MOBIUS function. Tasmeem Reza · 2 years, 7 months ago

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@Tasmeem Reza Yes...thats right👍👍 Good use of MOBIUS function Vinay Sipani · 2 years, 6 months ago

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@Vinay Sipani even cot(45)=1 Vamshi Krishna Kandula · 2 years, 7 months ago

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@Vinay Sipani even cotan(45)=1 Alamuru Ganesh · 2 years, 7 months ago

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@Alamuru Ganesh yup..right.👍👍 Vinay Sipani · 2 years, 7 months ago

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@Vinay Sipani 5 (mod 4) = 1 Mehul Arora · 2 years ago

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@Vinay Sipani \(\frac{d}{dx}(x+54)=1\) Tasmeem Reza · 2 years ago

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@Vinay Sipani 5-4=1 Mehul Arora · 2 years, 2 months ago

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@Vinay Sipani Woahh, allaww Noor Haadi · 2 years, 7 months ago

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Same thing as 5-4 but looks different \(\int _{ 4 }^{ 5 }{ dx } = 1\) Lol. X'D Vishnuram Leonardodavinci · 2 years, 7 months ago

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@Vishnuram Leonardodavinci yess....even this is possible👍👍 Vinay Sipani · 2 years, 7 months ago

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@Vishnuram Leonardodavinci Nicely done, didn't see that. Sharky Kesa · 2 years, 7 months ago

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\(\dfrac { Gamma(5) }{ 4! } =1\) Michael Mendrin · 2 years, 7 months ago

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@Michael Mendrin Could u explain what the gamma() function's purpose Tanya Gupta · 2 years, 7 months ago

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@Tanya Gupta 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 · 2 years, 7 months ago

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@Michael Mendrin Woah!!!...thank you so much!!! Tanya Gupta · 2 years, 7 months 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 · 2 years, 7 months ago

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@Michael Mendrin 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 · 1 year, 10 months ago

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@Michael Mendrin yeah...never thought of this...👌👍 Vinay Sipani · 2 years, 7 months ago

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@Michael Mendrin Aw yes. :-) Vishnuram Leonardodavinci · 2 years, 7 months ago

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\(\lfloor{\frac {5}{4}}\rfloor\) or \(\lceil{\frac {4}{5}}\rceil\) Sharky Kesa · 2 years, 7 months ago

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@Sharky Kesa In a similar way, \( \lfloor \sqrt[5]{4} \rfloor, \lfloor \sqrt[4]{5} \rfloor \) etc will also work. Chung Kevin · 2 years, 7 months ago

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@Chung Kevin Or \(\lfloor{\sqrt{\frac {5}{4}}}\rfloor\) and \(\lceil{\sqrt{\frac {4}{5}}}\rceil\) Sharky Kesa · 2 years, 7 months ago

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@Sharky Kesa Thas possible...greatest integer function..👍 Vinay Sipani · 2 years, 7 months ago

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@Sharky Kesa 5 and 4 are used twice Vikrant6 Bhatia · 2 years, 7 months ago

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@Vikrant6 Bhatia No, they're not. They are used only once in each expression. I have written them separately. Sharky Kesa · 2 years, 7 months ago

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@Sharky Kesa It's for Kevin's solution. Joshua Ong · 2 years, 6 months ago

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@Joshua Ong Same goes for Kevin's solution. Sharky Kesa · 2 years, 6 months ago

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@Sharky Kesa Ah yes ty I was misled too -_- Joshua Ong · 2 years, 6 months ago

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@Joshua Ong LOL :D Sharky Kesa · 2 years, 6 months ago

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\(5 \oplus 4 = 1\) Ammar Fathin Sabili · 2 years, 7 months ago

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@Ammar Fathin Sabili You need to describe the modulo number i.e.\(5 \bigoplus_84\) for which an extra 8 is required. Vinay Sipani · 2 years, 7 months ago

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@Vinay Sipani It's not modulo, but an XOR operation, :) Ammar Fathin Sabili · 2 years, 7 months ago

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@Ammar Fathin Sabili ohkk.....thats right....superb 👍👍👌 Vinay Sipani · 2 years, 7 months ago

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@Ammar Fathin Sabili Whats the sign between 5 and 4??? Tanya Gupta · 2 years, 7 months ago

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@Ammar Fathin Sabili this made my day....ahahahah Varshith Reddy · 2 years, 7 months ago

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\[ \ln \left({\frac{\exp{(5)}}{\exp{(4)}}}\right)=1 \] Zakaria Sellami · 2 years, 7 months ago

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@Zakaria Sellami Wow....superb !!Gud one👌👌

This one's right.

Edit it to Ln instead of log... Vinay Sipani · 2 years, 7 months ago

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@Vinay Sipani 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 · 2 years, 7 months ago

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

However Ln seems better...:) Vinay Sipani · 2 years, 7 months ago

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5 mod 4 =1 Tanya Gupta · 2 years, 7 months ago

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\(v_4(5!) = 1\) Michael Tang · 2 years, 7 months ago

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@Michael Tang Speechless....... Zi Song Yeoh · 2 years, 7 months ago

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@Michael Tang What is \(\nu\) function ??? Vinay Sipani · 2 years, 7 months ago

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@Vinay Sipani Highest power of a prime that divides something.In this case it is not used properly, because 4 is not a prime. Bogdan Simeonov · 2 years, 7 months 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 · 2 years, 7 months ago

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@Michael Tang yes it works... Vinay Sipani · 2 years, 7 months ago

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\( \frac{\phi(5)}{4} = 1\) Tan Li Xuan · 2 years, 7 months ago

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@Tan Li Xuan On a similar note of numerical functions, \(d(4)-d(5)=1\) where \(d(n)=\)the number of positive divisors of n. Xuming Liang · 2 years, 7 months ago

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@Tan Li Xuan yup...another solution.. Vinay Sipani · 2 years, 7 months ago

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

\(|cis(45°)|=1\) Alan Enrique Ontiveros Salazar · 2 years, 7 months ago

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@Alan Enrique Ontiveros Salazar yeah....cool solution...gud one ✌👍 Vinay Sipani · 2 years, 7 months ago

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Greatest integer(5/4) Kushagra Jaiswal · 2 years, 8 months ago

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@Kushagra Jaiswal Yes..this one is possible.

3 more ways are possible. Vinay Sipani · 2 years, 8 months ago

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@Vinay Sipani Signum(5+4), Signum(5×4) Signum(5÷4) Kushagra Jaiswal · 2 years, 8 months 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 · 2 years, 8 months ago

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signum(45),or anything which invlove 4 and 5(but real) Tejasvi Singh · 2 years, 7 months ago

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@Tejasvi Singh yes...signum function is possible...It is a function which always gives 1 for any constant. Vinay Sipani · 2 years, 7 months ago

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Gcd(5,4)=1 The easiest one Mardokay Mosazghi · 2 years, 7 months ago

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In programming languages (int)5/4=1 Hari Mohan · 2 years, 6 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, 6 months ago

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@Samuraiwarm Tsunayoshi Lawl is that too much... ==" Samuraiwarm Tsunayoshi · 2 years, 6 months ago

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@Samuraiwarm Tsunayoshi Where \(d(n)\) is the number of divisors of n and \(\sigma(n)\) is the sum of divisors of n. Samuraiwarm Tsunayoshi · 2 years, 6 months ago

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Is this possible 5 + 4i^2 N C · 2 years, 7 months ago

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@N C This gives 1 but extra 2 cant be used as in i^2. Vinay Sipani · 2 years, 6 months ago

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@Vinay Sipani Just write it like this: \(5+4i \times i=1 \) Zakaria Sellami · 2 years, 6 months ago

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@Zakaria Sellami Much bypass though. Joshua Ong · 2 years, 6 months 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 · 2 years, 6 months ago

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@Zakaria Sellami Yeah...now it's possible.. Gud 1👍👍 Vinay Sipani · 2 years, 6 months ago

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5 modulo 4=1 Basant K Jha · 2 years, 7 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, 7 months ago

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totient funtion of 5 / 4 Alamuru Ganesh · 2 years, 7 months ago

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@Alamuru Ganesh yeah...its possible

(Totient of 5)/4 Vinay Sipani · 2 years, 7 months ago

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5% 4 Saneel Velangkar · 2 years, 6 months ago

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Cot45= 1 Husain Kennedy · 2 years, 7 months ago

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5 = 101 (binary notation) 4 = 100 So. 5 xor 4 = 001 Kunal Krishna · 2 years, 7 months ago

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5 modulo 4 Debarati Biswas · 2 years, 7 months ago

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5%4=1 G C Keerthi Vasan · 2 years, 7 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, 7 months ago

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@Weerdhaval Chowgule Ya....and even c=5%4 Vinay Sipani · 2 years, 7 months ago

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tan 45 Rohan Lad · 2 years, 7 months ago

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  1. \(\lceil \frac{4}{5} \rceil\)
Happy Melodies · 2 years, 7 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, 7 months ago

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@Deepak Gowda Thank you...

Generating 0 to 100 will be more interesting..I think you should post a note on it... Vinay Sipani · 2 years, 7 months ago

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@Deepak Gowda Also post its link in this note as a comment... Vinay Sipani · 2 years, 7 months ago

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@Vinay Sipani Here, I've created a note for this. Kenny Lau · 2 years, 6 months ago

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(5+4)/(5+4) John Errol Obia · 2 years, 7 months ago

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@John Errol Obia you've broken the rules Priyesh Pandey · 2 years, 6 months 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 · 2 years, 7 months ago

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@Youssef Hafez \(\sum_{i=1}^{\infty}4×5^{-i}\)

The expression gives the value 1 but extra 1 and \(\infty\) cannot be used. Vinay Sipani · 2 years, 7 months ago

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5%4 Ishan Dixit · 2 years, 7 months ago

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5%4. Mohit Gupta · 2 years, 7 months ago

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5%4 (mod)=1 Dushyant Vyas · 2 years, 7 months ago

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(1) 5%4 Manoj Patial · 2 years, 7 months ago

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ceil(4/5),floor(5/4) Sushant Ranade · 2 years, 7 months ago

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gcd (4,5)=1 Sunitha Bhadragiri · 2 years, 7 months ago

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@Sunitha Bhadragiri what does ceil and floor mean Kaivalya Swami · 2 years, 7 months ago

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5%4 Jude D'silva · 2 years, 7 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, 7 months ago

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

Also, \(\frac{\varphi(5)}{4}=1\) Bogdan Simeonov · 2 years, 7 months ago

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@Bogdan Simeonov yep..The gcd(5,4) is the most obvious. Vinay Sipani · 2 years, 7 months 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 · 2 years, 7 months ago

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(5/4) × (4/5) = 1.25 x 0.8 = 1 QED M Bilal Giga · 2 years, 8 months ago

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@M Bilal Giga The condition is you cannot use 5 and 4 more than once. Vinay Sipani · 2 years, 8 months ago

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@Vinay Sipani Ah fair enough M Bilal Giga · 2 years, 8 months ago

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(5/4)*(4/5) Irisae Jade · 1 year, 10 months ago

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uuhgjjjjk Tergel Myagmarsaikhan · 1 year, 11 months ago

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

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5%4=1or equivalently 5mod4=1 Priyesh Pandey · 2 years 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, 1 month ago

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

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

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\(y\quad =\quad 54x\\ then\\ { [\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ] }!\\ =1\) Rudresh Tomar · 2 years, 6 months ago

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@Rudresh Tomar You cannot use 2... Vinay Sipani · 2 years ago

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⌊ln(5.4)⌋ Kenny Lau · 2 years, 6 months ago

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Tan(45)=1 Lina .... · 2 years, 6 months ago

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a^0 = 1 Vhie Yaa Jesus · 2 years, 6 months ago

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@Vhie Yaa Jesus Nope....0 not to be used. Vinay Sipani · 2 years, 6 months ago

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( 5 / 4 ) * ( 4 / 5 ) or ( 5 / 5 ) / (4 / 4) something like this :D Mario Medhat · 2 years, 6 months ago

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@Mario Medhat Nope...you cant use 5 and 4 two times. Vinay Sipani · 2 years, 6 months ago

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(5^2+4^2+4)/45 Sanjay Mohan · 2 years, 6 months ago

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((5×4)/5)/4 or ((4×5)/4)/5. They work Nathan Blanco · 2 years, 6 months ago

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Mine is easier 5/4 x 4/5 Hafizh Ahsan Permana · 2 years, 6 months ago

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Comment deleted Jun 29, 2014

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@Devendra Sethia Sorry, it is supposed to be (5X4) instead of (54) Devendra Sethia · 2 years, 6 months ago

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(4-5)^{2} Roushan Chandan · 2 years, 6 months ago

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@Roushan Chandan '-' sign should not be used and extra numbers cant be used. Vinay Sipani · 2 years, 6 months ago

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The 3 solution i no is Lint of 4/5 Zint of 5/4 Tan45 Shehzada Shehzada · 2 years, 7 months ago

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!0 Cleiston Rodrigues · 2 years, 7 months ago

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5×4=20.Then 20÷20=1 Kiran Dhamane · 2 years, 7 months ago

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5^{0} \times 4^{0} Dhruva Kothari · 2 years, 7 months ago

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@Dhruva Kothari Good one but you used 0 Zakaria Sellami · 2 years, 7 months ago

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@Dhruva Kothari can you please explain the notation....?? Charvi Vitthal · 2 years, 7 months ago

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@Charvi Vitthal It is 5 raised to 0 divided by 4 raised to 0 Weerdhaval Chowgule · 2 years, 7 months ago

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@Weerdhaval Chowgule ohkk... :) Charvi Vitthal · 2 years, 7 months ago

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5/4 Стэн Марш · 2 years, 7 months ago

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5 modules 4 = 1 Rajat Sharma · 2 years, 7 months ago

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5 \times 4 / 5\times 4 Vidul Ap · 2 years, 7 months ago

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@Vidul Ap 5 and 4 can be used only once... Vinay Sipani · 2 years, 7 months ago

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5%4 = 1 Ferdose Ashraf · 2 years, 7 months ago

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Write a comment or ask a question... 5!/(5*4!)=1 Aryan Tomar · 2 years, 7 months ago

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@Aryan Tomar No two times 5 Vinay Sipani · 2 years, 7 months 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 · 2 years, 7 months ago

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can i use concantenation?

\( \frac{(5|4)}{54} = \boxed{1} \) Barjuan Davis · 2 years, 7 months ago

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@Barjuan Davis You can use concatenations

But two times 5 and 4 not allowed. Vinay Sipani · 2 years, 7 months ago

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(cos 5) ^2 + (sin 5) ^2 = 1 Deepak Gowda · 2 years, 7 months ago

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@Deepak Gowda 2 cannot be used. Vinay Sipani · 2 years, 7 months ago

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We can use 5 XNOR 4 == 1 101 XNOR 100 == 1 What you say? Arun Gupta · 2 years, 7 months ago

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

But 5 xor 1 = 001. Vinay Sipani · 2 years, 7 months ago

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@Vinay Sipani Sorry my fault, It's not a valid solution. Solution should be like, we can not only use 5 and 4? ryte? Arun Gupta · 2 years, 7 months ago

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@Arun Gupta 5 and 4 to be used only once and no other numbers. Vinay Sipani · 2 years, 7 months ago

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5%4=1 what say guys ? Ajit Panada · 2 years, 7 months ago

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Dim x as integer; x=5/4 Dave Dave · 2 years, 7 months ago

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(5*4)^0 =1 Brahmam Meka · 2 years, 7 months ago

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@Brahmam Meka 0 not allowed and

5 and 4 not allowed twice. Vinay Sipani · 2 years, 7 months ago

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(4/5)X(5/4) Biswajit Mohanty · 2 years, 7 months ago

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Mod(5,4) Muhammad Riaz · 2 years, 7 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, 7 months ago

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abs(5/4) Piyush Patnaik · 2 years, 7 months ago

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@Piyush Patnaik Why not 5 mod 4 p^2

(Actually p^2 is Piyush Patnaik) Ashutosh Mahapatra · 2 years, 7 months ago

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5#/4! Ronq Vader · 2 years, 7 months ago

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1= 5!/(5×4!) Anshul Shivhare · 2 years, 7 months ago

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@Anshul Shivhare 5 and 4 only once... Vinay Sipani · 2 years, 7 months ago

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5-4 floor(5/4) ceiling(5/4) 54/54 Ramasubramaniyan Gunasridharan · 2 years, 7 months ago

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(factorial(5)/factorial(4))/5 M Kashif · 2 years, 7 months ago

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*5 mod 4 =1; *(5+4) mod 4=1; Sam Indhu · 2 years, 7 months ago

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@Sam Indhu 5 (mod 4) is possible but (5+4)(mod 4) is not possible...only one time 5... Vinay Sipani · 2 years, 7 months ago

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@Vinay Sipani oh....kk sry Sam Indhu · 2 years, 7 months 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 · 2 years, 7 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, 7 months ago

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-(4-5)=1 The mirror effect Tran Quan · 2 years, 7 months ago

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@Tran Quan No minus sign......... Utkarsh Dwivedi · 2 years, 7 months ago

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totient function of 4 x .5 Alamuru Ganesh · 2 years, 7 months ago

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@Alamuru Ganesh here 0.5 is not possible... Vinay Sipani · 2 years, 7 months ago

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5/4 remainder is 1 5mod4 is 1 Arun Sowri · 2 years, 8 months ago

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@Arun Sowri 5%4=1...Yes,thats one of the ways that I knew. Vinay Sipani · 2 years, 8 months ago

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Log54 to the base 54 Aman Chaudhary · 2 years, 8 months ago

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@Aman Chaudhary 5 and 4 can be used only once.. Vinay Sipani · 2 years, 8 months ago

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@Vinay Sipani (5 xor 4) in binary Dead Call · 2 years, 7 months ago

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@Dead Call Yes....This is possible even...gr8 Vinay Sipani · 2 years, 7 months 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 · 2 years, 5 months ago

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@Brendan Caseria yep..breaks the rule. Vinay Sipani · 2 years, 5 months ago

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f\left( x \right)=x\ f(5)-f(4)=1 Shrajan Vetcha · 2 years, 6 months ago

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[5/4] Shantnu Patlan · 2 years, 7 months ago

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Taking (5+4)- (4+4) = 1 Ahmad Bashir · 2 years, 7 months ago

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54/54 =1,45/45=1,5%4=1,(5*5)%4! Radha Krishnan B · 2 years, 7 months ago

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5^4 Sagar Sharma · 2 years, 7 months ago

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(54)/(54) Vidul Ap · 2 years, 7 months ago

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5 x 4 -19 Elita Zheng · 2 years, 7 months ago

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@Elita Zheng nvm... Can't have a - sign Elita Zheng · 2 years, 7 months ago

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(54)/(54) Brahmam Meka · 2 years, 7 months ago

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54/54 Kaivalya Swami · 2 years, 7 months ago

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(5×4)/(10×2) Rohan Chaudhary · 2 years, 7 months ago

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@Rohan Chaudhary 10 and 2 cant be used. Vinay Sipani · 2 years, 6 months ago

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I'LL BLOW ALL OF YOUR MINDS!!!! |4-5|=1 Nathan Blanco · 2 years, 6 months ago

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5^0 times 4^0 = 1 Vicneswaran Vicnes · 2 years, 7 months ago

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@Vicneswaran Vicnes Wrong answer 0 can't be used Sampad Kar · 2 years, 7 months ago

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@Vicneswaran Vicnes nope...0 cant be used. Vinay Sipani · 2 years, 7 months ago

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