Find the shortest expression to store 3+√(10) into Ans. The obvious way
Code: 3+√(10
is five bytes, but there's something shorter! For your reference, 3+sqrt(10) is about 6.1623.
I realize this can be solved using a Levin search ("try all possible programs"), but I'm hoping someone will find the solution a different way.
I suspect that the key here is to find a constant that is derived from √10 in some way, but so far I'm drawing a blank. I suspect the fact that 2π is close to 3+√10 is a red herring.
this is it a bit tough. my solution will probably be invalid, but it's pretty close....
3 bytes.
Code: √38
=
6.1644
it's about .0021 off, but I would say that's pretty darn good...
probably not the solution your looking for though 
Code: 6+Ans⁻¹
is 4 bytes but I'm pretty sure it doesn't count because you have to do it a few times.
Are you allowed to have "3+√(10" stored in Str1 beforehand and just use expr(Str1) as the code, or is that kind of cheap? This is harder than I thought it would be.
readroof2 wrote:
Are you allowed to have "3+√(10" stored in Str1 beforehand and just use expr(Str1) as the code, or is that kind of cheap? This is harder than I thought it would be.
That would probably be still as many bytes long as the expression, assuming that the calculator replaces Str1 by it's true value during calculations
AliceIsDead wrote:
readroof2 wrote:
Are you allowed to have "3+√(10" stored in Str1 beforehand and just use expr(Str1) as the code, or is that kind of cheap? This is harder than I thought it would be.
That would probably be still as many bytes long as the expression, assuming that the calculator replaces Str1 by it's true value during calculations
I made two different programs, one with 3+√(10 in it and the other with expr(Str1 with "3+√(10" already stored in Str1, and they both worked but the program with expr(Str1 was 4 bytes. However, I doubt this is the answer. I agree with Kerm that it probably has something to do with changing the √(10 part.
readroof2 wrote:
I made two different programs, one with 3+√(10 in it and the other with expr(Str1 with "3+√(10" already stored in Str1, and they both worked but the program with expr(Str1 was 4 bytes. However, I doubt this is the answer. I agree with Kerm that it probably has something to do with changing the √(10 part.
Like merging the 3 and the 10 under the same root...
I have been trying a lot of stuff and I still have no idea how to solve this.
I figured this out earlier:
x₂ - (x-1)₂ = x + (x-1)
Although √10 and √9 aren't consecutive numbers, 10 and 9 are...
AliceIsDead wrote:
readroof2 wrote:
I made two different programs, one with 3+√(10 in it and the other with expr(Str1 with "3+√(10" already stored in Str1, and they both worked but the program with expr(Str1 was 4 bytes. However, I doubt this is the answer. I agree with Kerm that it probably has something to do with changing the √(10 part.
Like merging the 3 and the 10 under the same root...
I have been trying a lot of stuff and I still have no idea how to solve this.
I figured this out earlier:
x₂ - (x-1)₂ = x + (x-1)
Although √10 and √9 aren't consecutive numbers, 10 and 9 are...
I also tried to make them one radical, but I couldn't remember if there was a way to. I will look up how to merge two radicals.
readroof2 wrote:
Are you allowed to have "3+√(10" stored in Str1 beforehand and just use expr(Str1) as the code, or is that kind of cheap?
It's a math puzzle, what do you think? ._.
hooloovoo's solution is clever, but there are a ton of errors that can come out of it depending on what Ans is... I doubt this'll help in solving, but is it a coincidence that 6.162277667^-1 is .1622776602 [and that sqrt(10)^-1==sqrt(10)/10]?
M. I. Wright wrote:
... but there are a ton of errors that can come out of it depending on what Ans is...
The only error I could pull out of it is if ans is 0. Otherwise, it always converges.
Michael2_3B wrote:
this is it a bit tough. my solution will probably be invalid, but it's pretty close....
3 bytes.
Code: √38
=
6.1644
it's about .0021 off, but I would say that's pretty darn good...
probably not the solution your looking for though
The cubed root of 234 is 4 bytes and 6.162240148, so very close. Any higher of an index and it would get over 5 bytes because cubed root has a 1 byte token, but the xth root needs two number input type things.
The closer I could get was √40. It is 6.32455532..., which is √10 + 3 with the decimal part *2
A hint and related puzzle:
Find the shortest expression to store the golden ratio, (1+√(5))/2, into Ans. The obvious way
Code: .5+.5√(5
is seven bytes, but there is something shorter!
To solve this you can either do the math, or find someone who already did...
I asked my brother about this, and mentioned hyperbolic trig. We did some mental math, and came up with " e to the arcshine of 3", which translated into real words is
Code: e^cosh⁻¹(3
3 bytes.
Hooloovoo wrote:
I asked my brother about this, and mentioned hyperbolic trig. We did some mental math, and came up with " e to the arcshine of 3", which translated into real words is
Code: e^cosh⁻¹(3
3 bytes.
That's 4 bytes (but still smaller than 5)
Code: e (1)
^ (2)
cosh⁻¹( (3)
3 (4)
Maybe I'm doing something wrong , but it doesn't give me 3+√(10 which is 6.1622..., instead this gives me 5.828427...
Hooloovoo, you've solved it!
Of course you mean
Code: e^(sinh⁻¹(3
which is still 3 bytes.
Yes, that's exactly what I mean. I just translated me and my brothers' arcshine silliness wrong.
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