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Full Version: (OT) Pandigital expression (HP-48,49,50g)
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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.

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.

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

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

Cheers

Thomas

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

DECIMAL POINT IS COMMA :-)

Cheers,

Gerson.

Quote:
DECIMAL POINT IS COMMA

Ditto!

forever and ever amen.

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 :-)

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 :-)

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 :-)

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

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!

```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

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

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.

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!

:D

Thank's !

I tried to find another pandigital expression for this without success

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.

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.

I'm late but :

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

In french date format of course ;)

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

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.