Challenge: Generate 24 in the X register / display

[Gene]

(09-08-2020 12:04 AM)Dwight Sturrock Wrote:  HP42S, 5 steps:

4.9
ENTER
ENTER
X
IP

Gene: That does indeed generate 24, but does not satisfy the basic rule on the initial post.

"Using a single digit repeated 3 and only 3 times..."

4.9 is not a single digit between 0 and 9.

[Valentin Albillo]

.
Hi, Gene & all:

Quote:Challenge: Using a single digit repeated 3 and only 3 times, produce the number 24 in the X register

As no one has submitted a solution for the HP-71B (as if !), here's a generic one I've created for it:

      DISP USING "^,DD";(digit+digit)/digit,FACT(RES+RES)

                   24

Simple as it is, notice the following:

      - it meets all requirements but as the HP-71B doesn't have an "X register" it simply puts 24 in the display
      - it works in any FIX, SCI or whatever mode so it puts in the display 24, not 2.4000E1 or 24.00
      - it doesn't use any other numbers at all, nor any variables
      - as per the requirements, it works for digit = 1,2,3,..., 9, but also you can replace digit by most any number, be it Pi, Sqrt(5), e^Pi^Pi, ...-, except digit = 0
      - for digit = 0, substitute digit above by, say, EXP(digit) or COS(digit), and there you are.
      - also, RES+RES could be instead RES*RES, RES^RES, and other variants.

This solution can be adapted easily to most RPN models, for instance:

      digit, ENTER, digit, +, digit, / , x^2, FACT

Thanks for the challenge and best regards.
V.

[pinkman]

My apologies for this answer: I did not have the time to participate, and before reading the above answers I post mine. Sorry if I’m repeating answers or giving some already found (and I guess I’m far from the best answers).
Tested on HP42s but did not want to use STO+X to make it work on 15c or other classic RPN.

That said, here are my attempts:

Code:


1 10^x 1 + 1 + ENTER +
2 10^x 2 / 2 / DSE
3 3 x^y 3 -
4 4 + 4 x^2 +
5 5 5 * DSE
6 6 6 + ENTER +
7 7 * 7 SQRT IP / IP
8 8 + 8 +
9 9 + LASTX + 9 SQRT -
0 0 10^x 10^x 0 e^x e^x * LASTX - IP

Now I can’t wait to see the answers for 9 and 0!

[pinkman]

And now I’ve read the above messages and noticed that the rules, apparently clear and simple, were not.
Was it asked to find a solution for each digit from 0 to 9 as I did, or the best solution using 1 of the digits?
I also understand that each digit had to be used 3 and only 3 times, and I respected the rule with a few cheating, letting the unused digits on the stack (ie. 5).

[Gene]

The goal was to use each digit exactly 3 times, no more and no less.

Ideally 10 solutions, one for 0 through 9.

A general solution is possible - get a number 4 showing in the display and use FACT or n! (if available on the model) to get to 24, but that may be more steps than another solution.

[Didier Lachieze]

A solution for 7, on the 42S, in 6 steps:

Code:

7
x^2
7
RCLx ST L
%
IP

(09-08-2020 04:21 PM)Gene Wrote:  The goal was to use each digit exactly 3 times, no more and no less.

So I assume that the RCLx ST L above is counting as the third use of the digit 7 .

[Dwight Sturrock]

(09-08-2020 01:40 PM)Gene Wrote:  

(09-08-2020 12:04 AM)Dwight Sturrock Wrote:  HP42S, 5 steps:

4.9
ENTER
ENTER
X
IP

Gene: That does indeed generate 24, but does not satisfy the basic rule on the initial post.

"Using a single digit repeated 3 and only 3 times..."

4.9 is not a single digit between 0 and 9.

Oops, think I was sidetracked by the exception for PI.

HP42S, 6 steps using 4 three times:

OCT
4
ENTER
ENTER
X
+

[pinkman]

Found new ideas

1) 5 steps

Code:


11
1
+
ENTER
+

2) 3 steps

Code:


22
2
+

3) 4 steps

Code:


33
3
X^2
-

4) 6 steps

Code:


44
4
x^2
LASTX
+
-

5) 7 steps

Code:


5
5
*
5
ENTER
/
-

6) 5 steps

Code:


66
LN
INT
6
*

7) 8 steps

Code:


7
7
*
7
SQRT
INT
/
INT

8) 5 steps

Code:


8
8
+
8
+

9) 7 steps

Code:


9
SQRT
9
*
9
SQRT
-

10) 10 steps

Code:


00
10^x
10^x
0
e^x
e^x
*
LASTX
-
IP

[Werner]

(41, 42) generic solution for d=1..9, shamelessly borrowing pinkman's idea:

Code:

 dd
 d
 ST+ Y
 /
 ST+ X

Cheers, Werner

[pinkman]

Excellent! This uses dd/d=11, thus (dd+d)/d=12
The same for 15c and others without STO X function:

Code:


dd 
d
+
LASTX
/
ENTER
+

[Hlib]

(hp-50)
#1 || 1 10^x EULER 1 %T 1 – ||
#2 || 2 DUP DUP ➝LIST ΣLIST ! ||
And a general solution for any three equal numbers
(including zero) placed on the stack:
|| N DUP DUP MAX SAME 10^x EULER ! ||
or
|| N DUP DUP MAX SAME 10^x √ e^x CEIL ||