Challenge: Generate 24 in the X register / display

[rprosperi]

Sometimes, it feels like there are more lawyers in here than calculator fans...

[Valentin Albillo]

(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.

[ndzied1]

On a 41c used 3 and 6 keystrokes.

[HP67]

6 keystrokes on HP 48.

Still waiting for Namir's no-key 41 solution

[Gene]

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... :-)

[ndzied1]

50g no digits, 3 steps

[HP67]

(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

[Paul Dale]

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).

[rprosperi]

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

[Sylvain Cote]

(09-07-2020 09:01 PM)rprosperi Wrote:  Embargo - lifted.

Actually not yet, it is 5PM CENTRAL TIME USA

[rprosperi]

(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...

[Hlib]

HP-50g, RPN mode. To ensure the least number of keystrokes I`ve 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

[Dwight Sturrock]

HP42S, 5 steps:

4.9
ENTER
ENTER
X
IP

[Fred Lusk]

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

[Paul Dale]

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

[Sylvain Cote]

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

[Sylvain Cote]

(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

[Namir]

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
*

[Didier Lachieze]

My solution for 2 on the 42S in 6 steps :

Code:

2
ENTER 
ENTER 
*
+
RCL* ST L

[ndzied1]

42S, digit 4, 7 steps, roundabout way. 4! 2 steps.

Code:

4
ENTER
ENTER
ENTER
/
-
PERM