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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
3 years, 2 months ago

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The four solutions that i know are:

1. The most basic: Tan(45)=1
2. 5%4=1 which is same as remainder when 5÷4
3. $$\Im^{4}=1$$,where $$\Im$$ is imaginary number.
4. Condone me after reading this...

$$\text{FIVE in Roman = V;}$$ $$\text{FOUR in Roman = IV.So,}$$ $\frac{4}{5}=\frac{IV}{V}=I=1$ · 3 years, 1 month ago

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$$5^{\mu(4)}$$ is also posible, where $$\mu$$ defines the MOBIUS function. · 3 years, 1 month ago

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Yes...thats right👍👍 Good use of MOBIUS function · 3 years ago

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even cot(45)=1 · 3 years, 1 month ago

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even cotan(45)=1 · 3 years, 1 month ago

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yup..right.👍👍 · 3 years, 1 month ago

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5 (mod 4) = 1 · 2 years, 7 months ago

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$$\frac{d}{dx}(x+54)=1$$ · 2 years, 7 months ago

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5-4=1 · 2 years, 9 months ago

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Woahh, allaww · 3 years, 1 month ago

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

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yess....even this is possible👍👍 · 3 years, 1 month ago

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Nicely done, didn't see that. · 3 years, 1 month ago

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

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Could u explain what the gamma() function's purpose · 3 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. · 3 years, 1 month ago

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Woah!!!...thank you so much!!! · 3 years, 1 month ago

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Mike, Don't you think the expression Gamma(t) = (t-1)! still has - which contradicts the basic condition.. Excellent knowledge though · 3 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 · 2 years, 4 months ago

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yeah...never thought of this...👌👍 · 3 years, 1 month ago

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Aw yes. :-) · 3 years, 1 month ago

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$$\lfloor{\frac {5}{4}}\rfloor$$ or $$\lceil{\frac {4}{5}}\rceil$$ · 3 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. · 3 years, 1 month ago

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Or $$\lfloor{\sqrt{\frac {5}{4}}}\rfloor$$ and $$\lceil{\sqrt{\frac {4}{5}}}\rceil$$ · 3 years, 1 month ago

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Thas possible...greatest integer function..👍 · 3 years, 1 month ago

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5 and 4 are used twice · 3 years, 1 month ago

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No, they're not. They are used only once in each expression. I have written them separately. · 3 years, 1 month ago

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It's for Kevin's solution. · 3 years ago

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Same goes for Kevin's solution. · 3 years ago

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Ah yes ty I was misled too -_- · 3 years ago

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LOL :D · 3 years ago

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$$5 \oplus 4 = 1$$ · 3 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. · 3 years, 1 month ago

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It's not modulo, but an XOR operation, :) · 3 years, 1 month ago

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ohkk.....thats right....superb 👍👍👌 · 3 years, 1 month ago

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Whats the sign between 5 and 4??? · 3 years, 1 month ago

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this made my day....ahahahah · 3 years, 1 month ago

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$\ln \left({\frac{\exp{(5)}}{\exp{(4)}}}\right)=1$ · 3 years, 1 month ago

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Wow....superb !!Gud one👌👌

This one's right.

Edit it to Ln instead of log... · 3 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 :) · 3 years, 1 month ago

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

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

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5 mod 4 =1 · 3 years, 1 month ago

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$$v_4(5!) = 1$$ · 3 years, 1 month ago

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Speechless....... · 3 years, 1 month ago

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What is $$\nu$$ function ??? · 3 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. · 3 years, 1 month ago

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I believe the function can still be used... This also works: $$v_5(\lceil \sqrt{4!} \,\rceil) = 1.$$ · 3 years, 1 month ago

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yes it works... · 3 years, 1 month ago

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$$\frac{\phi(5)}{4} = 1$$ · 3 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. · 3 years, 1 month ago

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yup...another solution.. · 3 years, 1 month ago

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

$$|cis(45°)|=1$$ · 3 years, 1 month ago

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yeah....cool solution...gud one ✌👍 · 3 years, 1 month ago

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

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Yes..this one is possible.

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

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Signum(5+4), Signum(5×4) Signum(5÷4) · 3 years, 2 months ago

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

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

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

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yes...signum function is possible...It is a function which always gives 1 for any constant. · 3 years, 1 month ago

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Gcd(5,4)=1 The easiest one · 3 years, 1 month ago

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

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

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Lawl is that too much... ==" · 3 years ago

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Where $$d(n)$$ is the number of divisors of n and $$\sigma(n)$$ is the sum of divisors of n. · 3 years ago

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Is this possible 5 + 4i^2 · 3 years ago

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@N C This gives 1 but extra 2 cant be used as in i^2. · 3 years ago

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Just write it like this: $$5+4i \times i=1$$ · 3 years ago

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Much bypass though. · 3 years ago

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Even like that is not correct; used the imaginary number $$i$$ while any number other than $$5$$ or $$4$$ cannot be used. · 3 years ago

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Yeah...now it's possible.. Gud 1👍👍 · 3 years ago

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5 modulo 4=1 · 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) · 3 years, 1 month ago

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

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yeah...its possible

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

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5% 4 · 3 years ago

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Cot45= 1 · 3 years, 1 month ago

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

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5 modulo 4 · 3 years, 1 month ago

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5%4=1 · 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) · 3 years, 1 month ago

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Ya....and even c=5%4 · 3 years, 1 month ago

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tan 45 · 3 years, 1 month ago

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1. $$\lceil \frac{4}{5} \rceil$$
· 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... · 3 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... · 3 years, 1 month ago

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Also post its link in this note as a comment... · 3 years, 1 month ago

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Here, I've created a note for this. · 3 years ago

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(5+4)/(5+4) · 3 years, 1 month ago

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you've broken the rules · 3 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 · 3 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. · 3 years, 1 month ago

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5%4 · 3 years, 1 month ago

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5%4. · 3 years, 1 month ago

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5%4 (mod)=1 · 3 years, 1 month ago

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(1) 5%4 · 3 years, 1 month ago

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

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gcd (4,5)=1 · 3 years, 1 month ago

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what does ceil and floor mean · 3 years, 1 month ago

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5%4 · 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 · 3 years, 1 month ago

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

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

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yep..The gcd(5,4) is the most obvious. · 3 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 ) · 3 years, 1 month ago

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

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The condition is you cannot use 5 and 4 more than once. · 3 years, 2 months ago

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Ah fair enough · 3 years, 2 months ago

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(5/4)*(4/5) · 2 years, 4 months ago

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uuhgjjjjk · 2 years, 5 months ago

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$$\dfrac{\gamma}{4!}$$ =$$1$$ · 2 years, 7 months ago

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

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$$5\quad mod\quad 4,\quad \left\lfloor \frac { 5 }{ 4 } \right\rfloor ,\quad \left\lceil \frac { 4 }{ 5 } \right\rceil ,\quad round\frac { 5 }{ 4 } ,round\frac { 4 }{ 5 } \\ \frac { \Gamma (5) }{ 4! } ,\quad cot(45deg)$$ · 2 years, 7 months ago

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

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4 mod(5)=1 · 2 years, 12 months ago

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$$y\quad =\quad 54x\\ then\\ { [\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } ] }!\\ =1$$ · 3 years ago

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You cannot use 2... · 2 years, 7 months ago

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⌊ln(5.4)⌋ · 3 years ago

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Tan(45)=1 · 3 years ago

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a^0 = 1 · 3 years ago

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Nope....0 not to be used. · 3 years ago

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( 5 / 4 ) * ( 4 / 5 ) or ( 5 / 5 ) / (4 / 4) something like this :D · 3 years ago

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Nope...you cant use 5 and 4 two times. · 3 years ago

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(5^2+4^2+4)/45 · 3 years ago

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

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Mine is easier 5/4 x 4/5 · 3 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) · 3 years ago

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(4-5)^{2} · 3 years ago

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'-' sign should not be used and extra numbers cant be used. · 3 years ago

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The 3 solution i no is Lint of 4/5 Zint of 5/4 Tan45 · 3 years, 1 month ago

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!0 · 3 years, 1 month ago

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

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

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Good one but you used 0 · 3 years, 1 month ago

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can you please explain the notation....?? · 3 years, 1 month ago

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It is 5 raised to 0 divided by 4 raised to 0 · 3 years, 1 month ago

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ohkk... :) · 3 years, 1 month ago

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5/4 · 3 years, 1 month ago

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5 modules 4 = 1 · 3 years, 1 month ago

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

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5 and 4 can be used only once... · 3 years, 1 month ago

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5%4 = 1 · 3 years, 1 month ago

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

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No two times 5 · 3 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 · 3 years, 1 month ago

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can i use concantenation?

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

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You can use concatenations

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

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

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2 cannot be used. · 3 years, 1 month ago

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We can use 5 XNOR 4 == 1 101 XNOR 100 == 1 What you say? · 3 years, 1 month ago

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

But 5 xor 1 = 001. · 3 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? · 3 years, 1 month ago

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5 and 4 to be used only once and no other numbers. · 3 years, 1 month ago

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5%4=1 what say guys ? · 3 years, 1 month ago

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

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(5*4)^0 =1 · 3 years, 1 month ago

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0 not allowed and

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

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(4/5)X(5/4) · 3 years, 1 month ago

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Mod(5,4) · 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. · 3 years, 1 month ago

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abs(5/4) · 3 years, 1 month ago

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Why not 5 mod 4 p^2

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

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5#/4! · 3 years, 1 month ago

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1= 5!/(5×4!) · 3 years, 1 month ago

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5 and 4 only once... · 3 years, 1 month ago

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5-4 floor(5/4) ceiling(5/4) 54/54 · 3 years, 1 month ago

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

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

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oh....kk sry · 3 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! · 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 , · 3 years, 1 month ago

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

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No minus sign......... · 3 years, 1 month ago

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

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here 0.5 is not possible... · 3 years, 1 month ago

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

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5%4=1...Yes,thats one of the ways that I knew. · 3 years, 1 month ago

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

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5 and 4 can be used only once.. · 3 years, 2 months ago

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(5 xor 4) in binary · 3 years, 1 month ago

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Yes....This is possible even...gr8 · 3 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? · 2 years, 11 months ago

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yep..breaks the rule. · 2 years, 11 months ago

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

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[5/4] · 3 years, 1 month ago

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

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

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5^4 · 3 years, 1 month ago

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(54)/(54) · 3 years, 1 month ago

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5 x 4 -19 · 3 years, 1 month ago

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nvm... Can't have a - sign · 3 years, 1 month ago

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(54)/(54) · 3 years, 1 month ago

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54/54 · 3 years, 1 month ago

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(5×4)/(10×2) · 3 years, 1 month ago

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10 and 2 cant be used. · 3 years ago

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

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

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Wrong answer 0 can't be used · 3 years, 1 month ago

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nope...0 cant be used. · 3 years, 1 month ago

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