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+--- Thread: Challenge: Generate 24 in the X register / display (/thread-15553.html)
RE: Challenge: Generate 24 in the X register / display - Gene - 09-08-2020 01:40 PM
(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.
RE: Challenge: Generate 24 in the X register / display - Valentin Albillo - 09-08-2020 03:09 PM
.
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.
RE: Challenge: Generate 24 in the X register / display - pinkman - 09-08-2020 03:38 PM
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 - IPNow I can’t wait to see the answers for 9 and 0!
RE: Challenge: Generate 24 in the X register / display - pinkman - 09-08-2020 04:00 PM
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).
RE: Challenge: Generate 24 in the X register / display - Gene - 09-08-2020 04:21 PM
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.
RE: Challenge: Generate 24 in the X register / display - Didier Lachieze - 09-08-2020 04:56 PM
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 .
RE: Challenge: Generate 24 in the X register / display - Dwight Sturrock - 09-08-2020 06:01 PM
(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
+
RE: Challenge: Generate 24 in the X register / display - pinkman - 09-08-2020 08:32 PM
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
/
INT8) 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
-
IPRE: Challenge: Generate 24 in the X register / display - Werner - 09-09-2020 06:39 AM
(41, 42) generic solution for d=1..9, shamelessly borrowing pinkman's idea:
Code:
dd
d
ST+ Y
/
ST+ XRE: Challenge: Generate 24 in the X register / display - pinkman - 09-09-2020 04:29 PM
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
+RE: Challenge: Generate 24 in the X register / display - Hlib - 09-09-2020 08:14 PM
(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 ||