Challenge: Generate 24 in the X register / display
09-07-2020, 01:26 PM
Post: #21
 rprosperi Super Moderator Posts: 5,254 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
Sometimes, it feels like there are more lawyers in here than calculator fans...

--Bob Prosperi
09-07-2020, 02:30 PM
Post: #22
 Valentin Albillo Senior Member Posts: 811 Joined: Feb 2015
RE: Challenge: Generate 24 in the X register / display
(09-07-2020 01:26 PM)rprosperi Wrote:  Sometimes, it feels like there are more lawyers in here than calculator fans...

Math fans, scientists and engineers, all of them tend to value precision, exactness and accuracy and abhor ambiguity. Lawyers, not so much.

Regards.
V.

All My Articles & other Materials here:  Valentin Albillo's HP Collection

09-07-2020, 02:36 PM
Post: #23
 ndzied1 Member Posts: 110 Joined: Apr 2014
RE: Challenge: Generate 24 in the X register / display
On a 41c used 3 and 6 keystrokes.
09-07-2020, 02:42 PM
Post: #24
 HP67 Senior Member Posts: 655 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
6 keystrokes on HP 48.

Still waiting for Namir's no-key 41 solution

It ain't OVER 'till it's 2 PICK
09-07-2020, 03:02 PM
Post: #25
 Gene Moderator Posts: 1,251 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
HP67... remember, six keys for a solution using which number from 0 - 9 ?

There are 10 scenarios to be solved here. What is a solution using the number 1 three and exactly three times? Same for 0. Same for 7, etc.

I suspect Namir's solution is using no digits at all. That's fine, but does not remove the scenarios above... :-)
09-07-2020, 03:34 PM
Post: #26
 ndzied1 Member Posts: 110 Joined: Apr 2014
RE: Challenge: Generate 24 in the X register / display
50g no digits, 3 steps
09-07-2020, 06:39 PM
Post: #27
 HP67 Senior Member Posts: 655 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
(09-07-2020 03:02 PM)Gene Wrote:  HP67... remember, six keys for a solution using which number from 0 - 9 ?

There are 10 scenarios to be solved here. What is a solution using the number 1 three and exactly three times? Same for 0. Same for 7, etc.

I suspect Namir's solution is using no digits at all. That's fine, but does not remove the scenarios above... :-)

Oh well I should have known. Any time I think I understand a problem in math of any kind it means I didn't understand it

It ain't OVER 'till it's 2 PICK
09-07-2020, 09:01 PM
Post: #28
 Paul Dale Senior Member Posts: 1,750 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
My no digits solution is three steps:
Code:
01 pi 02 e^x 03 CEIL

Without CEIL, it's four steps (on a 41):
Code:
01 pi 02 e^x 03 INT 04 ISG ST X

This provides a limit on solutions because the digits can be entered first and ignored:
Code:
01 0 02 0 03 0 04 pi 05 e^x 06 CEIL

I.e. there is a digit independent way of getting the result in six bytes/steps assuming all the used functionality is available on the device in question. Okay, pi isn't permitted since it is a constant but that leads onto:

For digits 1 - 9, there is an eight step solution.

Assume the digit is d:
Code:
01 d 02 ENTER 03 d 04 + 05 d 06 / 07 x^2 08 x!

Since we're aiming for the fewest steps, having this limit sets a bar -- not necessarily a very low bar but a bar. This doesn't mean that longer solutions aren't interesting. There is also an eight step solution for the digit 0.

On the other end of the scale, we must use each digit thrice and doing so cannot get the answer of 24. Therefore, the minimal program must be 4 or more steps/bytes. I suspect it has to be more than 4 in all cases (but no doubt will be proven wrong).
09-07-2020, 09:01 PM
Post: #29
 rprosperi Super Moderator Posts: 5,254 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
Embargo - lifted.

For the 41/42 and select other RPN models.

5
ENTER
ENTER
*
DSE X

5 steps , 8 bytes
16 bytes with 1-char global label and an END

--Bob Prosperi
09-07-2020, 09:20 PM (This post was last modified: 09-07-2020 09:20 PM by Sylvain Cote.)
Post: #30
 Sylvain Cote Senior Member Posts: 1,766 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
(09-07-2020 09:01 PM)rprosperi Wrote:  Embargo - lifted.
Actually not yet, it is 5PM CENTRAL TIME USA
09-07-2020, 09:47 PM (This post was last modified: 09-07-2020 09:47 PM by rprosperi.)
Post: #31
 rprosperi Super Moderator Posts: 5,254 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
(09-07-2020 09:20 PM)Sylvain Cote Wrote:  Actually not yet, it is 5PM CENTRAL TIME USA

Dang. Gene, when are you going to move to the East coast?

Anyhow, I'll be on a family monthly zoom then, plus I suspect this is not such an insightful solution that it will ruin anyone's day...

--Bob Prosperi
09-07-2020, 10:51 PM (This post was last modified: 09-07-2020 11:21 PM by Hlib.)
Post: #32
 Hlib Member Posts: 242 Joined: Jan 2015
RE: Challenge: Generate 24 in the X register / display
HP-50g, RPN mode. To ensure the least number of keystrokes Ive made a custom
soft menu for four functions: DUP, SQ(x^2), !(factorial), NOT.
{ DUP SQ ! NOT } CST STO [LS] [MODE] Thus number of steps in the solution match the keystrokes.
The universal chain N DUP + N ÷ SQ ! (seven clicks) comes up to every number except zero.
But in some particular cases, this can be made more shorter.
#9 24=√9×9–√9 || 9 √ 9 × 9 √ – || 7 steps(clicks)
#8 24=8+8+8 || 8 DUP + 8 + || 5 steps(clicks)
#7 24=(((7+7)÷7)^2)! || 7 DUP + 7 ÷ SQ ! || 7
#6 24=6^2–6–6 || 6 SQ 6 – 6 – || 6
#5 24=5^2–5÷5 || 5 SQ 5 DUP ÷ – || 6
#4 24=4^2+4+4 || 4 SQ 4 + 4 + || 6
#3 24=3^3–3 || 3 DUP y^x 3 – || 5
#2 24=(((2+2)÷2)^2)! || 2 DUP + 2 ÷ SQ ! || 7
#1 24=(((1+1)÷1)^2)! || 1 DUP + 1 ÷ SQ ! || 7
#0 24=... || 0 NOT 0 NOT + 0 NOT ÷ SQ ! || 10
09-08-2020, 12:04 AM
Post: #33
 Dwight Sturrock Member Posts: 136 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
HP42S, 5 steps:

4.9
ENTER
ENTER
X
IP
09-08-2020, 12:18 AM (This post was last modified: 09-08-2020 12:19 AM by Fred Lusk.)
Post: #34
 Fred Lusk Junior Member Posts: 12 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
I shortened my generic DM-42 program again. Now it is 10 steps. This program takes any single-digit number sitting in the X-register (or any number, positive, negative, or zero, for that matter), makes three copies in the stack (putting the number in X into Y and Z also), then uses all three numbers to create the number 24.

01 LBL "T4"
02 ENTER
03 ENTER
04 +
05 +
06 SIGN
07 RCL+ ST X
08 RCLx ST X
09 N!
10 END

If you preload the stack with the same number in X, Y, and Z, then delete steps 02 and 03, which leaves an 8-step program.

The following program will take ANY number in the X-register and convert it to 24. It works like the previous program, but it's simpler because it only has to deal with one number.

01 LBL "TF"
02 SIGN
03 RCL+ ST X
04 RCLx ST X
05 N!
06 END

...Fred
09-08-2020, 12:33 AM
Post: #35
 Paul Dale Senior Member Posts: 1,750 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
My solution for 4 is:

Code:
4 4 ENTER 4 n!

The first two 4's and the command after doing nothing.

For zero (8 steps):

Code:
0 0 COS 0 n! + x^2 n!

Pauli
09-08-2020, 02:49 AM (This post was last modified: 09-08-2020 02:51 AM by Sylvain Cote.)
Post: #36
 Sylvain Cote Senior Member Posts: 1,766 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
My solution for value 3 is: (HP-41 → 5 operations, 7 keystrokes, no unused data is left on the stack, Z & T are preserved)
Code:
3 ENTER YˆX LastX -

My solution for value 4 is: (HP-41 → 6 operations, lots of keystrokes, no unused data is left on the stack, Z & T are preserved)
Code:
4 FACT LastX * LastX /

My solution for value 5 is: (HP-41 → 6 operations, 8 keystrokes, no unused data is left on the stack, T is preserved)
Code:
5 xˆ2 LastX ENTER / -

Sylvain

Edit: typos
09-08-2020, 03:01 AM
Post: #37
 Sylvain Cote Senior Member Posts: 1,766 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
(09-08-2020 12:18 AM)Fred Lusk Wrote:  I shortened my generic DM-42 program again. ...
Code:
01 LBL "T4" 02 ENTER 03 ENTER 04 + 05 + 06 SIGN 07 RCL+ ST X 08 RCLx ST X 09 N! 10 END
Brilliant!

Here is an adapted version for the HP-41 and which also now preserve Z & T .
Code:
01 LBL "T4" 02 ENTER 03 + 04 LastX 05 + 06 SIGN 07 ST+ ST X 08 ST* ST X 09 FACT 10 END

Sylvain
09-08-2020, 04:04 AM
Post: #38
 Namir Senior Member Posts: 823 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
Using 1 only once
===========

Code:
1 10^x LASTX STO+X STO+Y *

Using NO Digit
=========

Code:
CLX 10^x 10^x LASTX STO+X STO+Y *
09-08-2020, 05:22 AM
Post: #39
 Didier Lachieze Senior Member Posts: 1,449 Joined: Dec 2013
RE: Challenge: Generate 24 in the X register / display
My solution for 2 on the 42S in 6 steps :
Code:
2 ENTER  ENTER  * + RCL* ST L
09-08-2020, 10:51 AM (This post was last modified: 09-08-2020 10:57 AM by ndzied1.)
Post: #40
 ndzied1 Member Posts: 110 Joined: Apr 2014
RE: Challenge: Generate 24 in the X register / display
42S, digit 4, 7 steps, roundabout way. 4! 2 steps.
Code:
4 ENTER ENTER ENTER / - PERM`
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