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Post a number with an interesting property

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Rudin
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29 Nov 2015, 9:43 pm

31=5x5+5+5/5


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Rudin
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29 Nov 2015, 9:51 pm

32=(5/5+5/5)^5


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30 Nov 2015, 4:10 pm

Rudin wrote:
32=(5/5+5/5)^5


This one seems particularly elegant and pleasing to me.



Rudin
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30 Nov 2015, 4:42 pm

Adamantium wrote:
Rudin wrote:
32=(5/5+5/5)^5


This one seems particularly elegant and pleasing to me.


Thank you.


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Earthling
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01 Dec 2015, 11:37 am

33 = (5!-5)/5+(5+5)
Tried yesterday, didn't find a solution.
Why this took me so long to come up with, I have no idea.



Earthling
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01 Dec 2015, 3:15 pm

34 = 5!/5+sqrt(5*5)+5



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01 Dec 2015, 3:17 pm

35 = 5*5+5+sqrt(5*5)



Adamantium
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02 Dec 2015, 1:49 pm

Rudin wrote:
6=5+5/5+(5-5)


For this one, I prefer 6=5!/(5+5+5+5)



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03 Dec 2015, 5:31 pm

An interesting article on the computational expense a computer must put forward for different operations.

http://streamcomputing.eu/blog/2012-07-16/how-expensive-is-an-operation-on-a-cpu/

For our purposes:
Addition (1)
Subtraction (1)
Multiplication (4)
Division (10)
Pow (100)
Square Root (Highly variable depending on processor implementation)

So the computer would always run faster by preferring not to use powers or roots.


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03 Dec 2015, 9:57 pm

Adamantium wrote:
Rudin wrote:
6=5+5/5+(5-5)


For this one, I prefer 6=5!/(5+5+5+5)



So, while I agree with you that the latter is more aesthetically pleasing, it is objectively inefficient. I think it is because there is more action, where 5!/20=6 provides more revelation than 6+1+0, so the inefficiency is itself entertaining, yet in solving for efficiency, the entire problem set seems again exciting.

The original 4 fours was a contest held by Ruth Carver and the preferred answer was the one that used the least operations. A more human measure of efficiency as these operations are essentially equivalent to the human mind. The original contest also ran from 0-100.


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Earthling
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05 Dec 2015, 8:23 pm

Hm. Genuinely can't come up with the solution for 36.



Rudin
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06 Dec 2015, 9:02 am

I came up with this one all by myself:

36=((5#)/5)^((5+5)/5)

Where 5# is 5 primorial, or the product of all the primes up to 5 (including 5).

5#=2x3x5
5#/5=6
(5+5)/5=2

6^2=36


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-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


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06 Dec 2015, 9:53 am

37=5#+5+(5+5)/5


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Earthling
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06 Dec 2015, 11:39 am

Hacks! But I'm glad you found a solution. :P

38 = (5!+5!)/5-(5+5)



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06 Dec 2015, 12:53 pm

45 and 54 are both divisible by 9

2 and 5 are the only prime numbers ending in 2 and 5

Also 807 for personal reasons: I was born at 8:07, weighed 8'7, and the last three digits of my student ID is 807.


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07 Dec 2015, 1:55 pm

Earthling wrote:
Hm. Genuinely can't come up with the solution for 36.


Heh.
Me too. I was waiting to see what more mathematically accomplished minds would come up with.
5# is new to me. Very interesting.