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(OT) Pandigital expression (HP-48,49,50g)



#2

Today is Sunday, but it's also the national date for some members of this forum. The following is kind of a celebration. Notice all digits from 0 through 9 are present and have been used only once. Perhaps FIX 6 should be used for proper day format.

Congratulations !

Edited to correct a language mistake


Edited: 14 July 2013, 4:52 p.m.


#3

hmm. i'm out by nearly a millenium.

> (0!+sqrt(2)+14*14/75!/(10^6+89))^3
14.07106781186547524400845

must be this mystery (-,75) thing?

any hints.


#4

Quote:
must be this mystery (-,75) thing?

For you probably rather (-.75)! = 3.62560990822.

Cheers

Thomas


#5

Gamma(1/4) would be nicer, but then 1 and 4 had already been used.

DECIMAL POINT IS COMMA :-)

Cheers,

Gerson.


#6

Quote:
DECIMAL POINT IS COMMA


Ditto!


forever and ever amen.


#7

thank you!

the flux capacity is now fixed!

> (0!+sqrt(2)+14*14/-.75!/(10^6+89))^3
14.07201300094483189388136

for a while i was thinking (-1,75)! ie (-1+75i)! which doesnt end up in our spacetime even :-)


#8

Wolfram Alpha will understand (0!+Sqrt[2]+Sq[14]/((-.75)!*(Alog[6]+89)))^3.
Originally pandigital expressions would involve only arithmetic operators, but I think the use of Sq, Sqrt etc., when available, makes things a bit more interesting. Sure this is a futile puzzle, but I didn't spend more than thirty minutes on this one :-)

#9

Too bad most programming languages don't have this feature. Back in the day I changed a few bytes in the ROM of my MSX computer. The result was fair enough :-)

#10

Thanks, this is a nice one! I'm curious about the methodology you used to get it...


#11

Quote:
I'm curious about the methodology you used to get it...

Me too, especially after learning that it only took you 30 minutes to find it. Nicely done!

#12

keystrokes                       display          comments

14.072013 STO A 14.072013
LN 2.64418793126 ~ pi^2/6 + 1
pi ENTER * 6 / 1 + - 1/X +/- 1340.23897721 nothing interesting after trying a
few functions and multiples
RCL A sqrt sqrt sqrt sqrt 1.1797018602 again, nothing interesting here
RCL A 3 1/x y^x 2.41426761738 ~ sqrt(2) + 1 -- this looks promising
2 sqrt - 1 - 1/x STO B 18499.6728333
3 * 55499.0184999 here we have

(sqrt(2) + 1 + 3/55499)^3 = 14.0720130004

but the 5-digit constant is almost as long
as the number we want to represent, also
it is not interesting. So let's try other
multiples
RCL B ENTER ENTER ENTER + 36999.3456666
+ + + + + + + + + + + + + 277495.092497

... (very fast keystrokes, I may have missed
some interesting results)

+ + + + + + + + + + STO C 3625935.87485 the first four digits match those of
gamma(1/4)
4 1/x 1 - x! / 1000089.9067 now we have

(196/(gamma(1/4)*(10^6 + 90)) + sqrt(2) + 1)^3

= 14.0720129999

Again, not interesting enough, but after
noticing 196 = 14^2 and gamma(1/4) = (-0.75)!
we can try a pandigital expression. There are
repeated digits (0, 1 and 2) and 8 is missing.
Replacing 90 with 89 solves the latter and
eliminates one repeated 0, 1 can be written as
0! and 14^2 as Sq(14). Also Alog(x) can be used
for 10^x, so we finally have

(Sq(14)/((-.75)!*(Alog(6) + 89)) + Sqrt(2) + 0!)^3
14 ENTER * .75 +/- x! / 6 10x
89 + / 2 sqrt + 0 x! + 3 yx
DISP FIX 6 14.072013 = 14.0720130009

Calculator: HP-32SII
Shifts have been omitted in the keystrokes listing above


#13

Quote:
3625935.87485 the first four digits match those of gamma(1/4)

Of course we all know that by heart. Let's be honest: who would not think immediately of that?
Gerson, you're just amazing!

Cheers

Thomas


#14

Quote:
Quote:
3625935.87485 the first four digits match those of gamma(1/4)

Of course we all know that by heart.


Well, at least the first few digits of a few constants we all do.

Not exactly a scientific methodology, but I guess W|A is not capable of this kind of thing [yet] :-)

Cheers,

Gerson.

#15

Quote:
Of course we all know that by heart.

You literally took the words out of my mouth. I'm still amazed by Gerson's procedure!

#16

A similar "method" yielded 'e*XROOT(12,e^(-3*4)+5.6789)' four years ago (this can be appended to '0+' to include all 10 digits, in ascending order!). And that took only 5 minutes :-)
It was only a matter of luck in both occasions, though. No idea for this year's Pi Approximation Day...

Cheers,

Gerson.

#17

:D

Thank's !

I tried to find another pandigital expression for this without success


#18

I don't think I would have found this one if I had started by trying to find it in the beginning. As I said, I was lucky I came up with an almost ready-made pandigital expression :-)

Cheers,

Gerson.

#19

I'm late but :

'SQ(4!-1)*2*7*(3*6+9-8)-5^0'

In french date format of course ;)


#20

Très bien !
And you already have the ones for the next two years :-)


#21

To find this, I use the FACTORS command of the 50G (or the ifactors of the Prime):

140713=140714-1

140713=2*7*19*23²-1

Edited: 19 July 2013, 6:01 a.m.


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