[VA] Short & Sweet Math Challenge #25 "San Valentin's Special: Weird Math"

[Nihotte(lma)]

(02-14-2021 08:58 PM)Valentin Albillo Wrote:   
Hi, all !   Happy San Valentín 2021 to all of you !  
 
...
That's all. Enjoy ! ... and that's an order !

V. 

UPDATED 2021.02.19 - 04.10PM to comply with the mention : Please do NOT include CODE panels in your replies to this thread

Hi,

Just to say, I've taken part of the challenge too !
However, I've progressed more slowly than you all...

For a. and b. points

I began with my HP35s :

** LBL V
INPUT S // 1 for stop
INPUT L // 100000 for loops
CLΣ
1
SEED
RCL L
STO I
009 CLx
STO J
STO C
012 1
STO + J
RANDOM
STO + C
RCL C
RCL S
x > y
GTO V012
0
RCL J
Σ+
DSE I
GTO V009
RCL L
RCL S
x-mean
RTN


XEQ V001
with S=1 and L=1E5 gave 2.71959 about 6 hours later

Then, I've brought out my 48G

<<
DEPTH DROPN
0 'SUM' STO
SEED RDZ
1 LOOPS
FOR i
0 DUP
DO
SWAP
1 +
SWAP
RAND +
DUP
TOP
UNTIL >= END
DROP 'SUM' STO+
NEXT
TOP LOOPS SUM OVER /
>>

with :
VAW is the program above
1 'TOP' STO // 1, 2 .. 20
1 'SEED' STO
100000 'LOOPS' STO
And the run of VAW gives
1
100000
2.71959
in the stack
and SUM is 271959

The result appears more rapidly than with the HP35s, of course
6x faster, perhaps

Unsurprisingly, my results match those of robve's post for the successive limit values ​​1, 2 .. 20 retained


------


The result for a limit of 1 seems to be close to e.
But, I've tested something on my HP10BII+
I decided to enter all couple of result by Σ+ in the calculator

C STAT
1 INPUT 2.71959 and Σ+
2 INPUT 4.67827 and Σ+
2.021 INPUT 4.71806 and Σ+
3 INPUT 6.66808 and Σ+
pi INPUT 6.95027 and Σ+
4 INPUT 8.66601 and Σ+
5 INPUT 10.66641 and Σ+
5+1/6 INPUT 10.99947 and Σ+
10 INPUT 20.65914 and Σ+
15 INPUT 30.66700 and Σ+
20 INPUT 40.66927 and Σ+
then,
[BLUE] REGR and [-] to select 0 - bESt Fit [INPUT]
and,
2 [ORANGE] ŷ,m displaying bESt Fit with the choice of 1 - LinEAr and the result of 4.6773856...
followed by [ORANGE] ^x,r resulting in 2 and [SWAP] giving 0,999999... as a correlation coefficient to describe the goodness of the fit.

Now here is where I am going with my initial idea :
1000 [ORANGE] ŷ,m 1999.68225...
100000 [ORANGE] ŷ,m 199900.966545...
200000 [ORANGE] ŷ,m 399801.25371...
1E9 [ORANGE] ŷ,m 1999002872.33...
9999999999 [ORANGE] ŷ,m 19990028715,2...
I don't know what to think but, it's giving a result near of 2*x decreased by something that is proportional to x (based on m, in fact) !!!