Consider the following keystroke sequences:

6 ENTER ENTER / - 3 ENTER . 3 / *x*^{y} 9 ENTER ENTER / - * 9 / 6 ENTER 3 / ENTER + 3 ENTER . 3 / *x*^{y} ENTER + 9 / 1/x -

and

3 0 ENTER 3 / pi *x*^{y} 3 sqrt 9 0 6 0 ENTER 3 0 / 3 0 - + 3 0 * 3 0 + pi 3 0 / + 3 sqrt / 3 sqrt 3 / + - 6 ENTER 9 / 3 0 / -

Both produce the same numerical result on the display (you'll have to key either one in to find out what it is). The more straightforward sequence is 36 keystrokes long. The somewhat exotic one is 49 keystrokes long. The goal is to find equivalent keystrokes sequences, the shortest the best, but interesting sequences using transcendental functions are welcome as well.

Rule: Use *only* keys in the first and last rows and in the first and last columns.

For test purpose only, you can use an HP-45 (just remember to replace *x*^{y} with *x<>y y*^{x}).

Have fun! :-)

Short (20 keystrokes) but not interesting:

9 9 9 9 9 . 9 9 9 9 9 ENTER . 0 0 0 0 9 1/x -

May I propose a near short keystroke sequence, but a byte more transcendental ?

N° Key

001 6

002 ENTER^

003 ENTER^

004 /

005 -

006 ENTER^

007 ENTER^

008 +

009 x^y

010 ENTER^

011 LOG

012 3

013 +

014 1/x

015 ENTER^

016 ENTER^

017 /

018 +

019 /

(simulated on an HP-41C)

*Edited: 1 Aug 2012, 4:17 a.m. *

Forget this post. I need to wake up first...

*Edited: 1 Aug 2012, 4:14 a.m. *

The HP-41CV displays a 9 in the last position, as expected. The HP-35 returns 88888.88933. The following "nice-try" solution is slightly shorter and a tad closer (88888.88895), but cannot beat Katie's clever solution above.

3 ENTER .3 / 933699 + 33 / pi *

Well, if not that funny at least it is good enough to dust off our classic calculators :-)

*Edited: 1 Aug 2012, 5:00 p.m. *

This is working with an HP 35 app for the iPad/iPod Touch/iPhone named rpn-35, I manged to get 88888.89161:

999 ENTER + 6 ENTER 3 ÷ 9 * 6 ENTER 3 ÷ 9 ÷ + 9 * - 1/x

6 ENTER 3 ÷ pi * 3 ENTER ÷ 9 + ÷ +

6 ENTER 3 ÷ 9 + 3 + ENTER ÷ 3 + * +

3 x<>y x^y

8/2/2012. Update: This first routine is not correct. Sorry. :(.

The following routine yields 88888.88894:

3 ENTER ÷ 99 + 3 *

3 ENTER ÷ 6 + 1/x +

3 ENTER ÷ 3 + 3 ENTER ÷ 9 + * 6 +

99999 ÷

- 6 ENTER 3 ÷ - 6 ENTER 3 ÷ x<>y x^y

It seems that I am stuck on 88888.88894: (47 keystrokes)

99 ENTER 3 * 3 ENTER ÷ +

9 ENTER 3 ENTER ÷ - 1/x +

3 SQRT 99 ÷ +

999 ENTER 9 - 3 - 9,999,9999 ÷ -

6 ENTER 3 ÷ x<>y x^y

A shorter routine to 88888.88894: (43 keystrokes)

99 ENTER 3 x pi ln +

300 ENTER 6 * 633 + 99 - 3 ENTER ÷ -

3 ENTER ÷ 999,999 + ÷ -

6 ENTER 3 ÷ x<>y x^y

*Edited: 2 Aug 2012, 9:17 a.m. after one or more responses were posted*

Longer (31 keystrokes), but perhaps interesting:

9 6 ENTER 6 / pi 9 0 ENTER 6 - 1/*x* 6 - *e*^{x} - *x*^{y} . 9 ENTER 6 / - 3 ENTER ENTER . 3 / *x*^{y} /

I've checked your sequences on the real HP-35 and the results match, except for the first one: 15.92693176 (unless I am doing something wrong). Notice x<>y is located in the third row (and in the second column), so it should not be used. By the way, if you happen to have a calculator like that, on which only the keys in the periphery work, I would advise you to have it fixed or buy a replacement at the usual place. Do not trust in pictures showing all eights though :-)

*Edited: 2 Aug 2012, 12:05 a.m. *

Well, this is an interesting exercise.

I was out of my regular office desk and have had no access to the simulators have on my regular PC system. So I have not tried my code of any simulator except the HP41C.

I was surprise to see that first/last row/column functions on HP-41 are nearly the same as on HP35/45's keyboard. Ah the good classic designs consistency!

In fact, the biggest challenge, for me, was to determine the 'secret' final result. Because you need so much extra keystrokes on the HP-35, I already suspected being out of goal by a decimal fraction!

I like the recreation of this type, dusting out oldies is always a good idée, this kept collections in true living conditions (as well as owner's brain !).

Thanks.

Quote:

I was surprise to see that first/last row/column functions on HP-41 are nearly the same as on HP35/45's keyboard. Ah the good classic designs consistency!

You're right! Perhaps we could extend the exercise to the HP-45, the HP-41 and other calculators:

shift Pi 9 0 ENTER 6 - 1/x 6 - e^x - 9 6 ENTER 6 / shift y^x . 9 ENTER 6 / - 3 shift 10^x / (HP-45, 29 keystrokes)
shift pi 9 0 ENTER 6 - 1/x 6 - shift e^x - 9 6 ENTER 6 / shift y^x . 0 3 + 3 shift 10^x / (HP-41, 28 keystrokes)

Regards,

Gerson.

Quote:

I've checked your sequences on the real HP-35 and the results match, except for the first one: 15.92693176 (unless I am doing something wrong). Notice x<>y is located in the third row (and in the second column), so it should not be used. By the way, if you happen to have a calculator like that, on which only the keys in the periphery work, I would advise you to have it fixed or buy a replacement at the usual place. Do not trust in pictures showing all eights though :-)

UGG - The swap key is in all of them - I was never good at these puzzles. :(. Had fun though - I will have to try again.

I was using an emulator, I don't own an actual HP 35 (classic).

*Edited: 2 Aug 2012, 9:24 a.m. *

Hello Eddie,

You can use the HP-45 Simulator at the Museum:

http://www.hpmuseum.org/simulate/sim45.htm

The numerical routines have the same accuracy on both calculators, just remember to use the [x<>y] and [y^x] keys to simulate the [x^y] key. As an alternative exercise, other 10-digit HP calculators can be tried using their specific functions and degree of accuracy to accomplish the same goal (as long as only the peripheral keys are used).

Regards,

Gerson.