Posts: 2,761
Threads: 100
Joined: Jul 2005
In case you're wondering about the title, this is kind of a little challenge: try to find the shortest RPN keystroke sequence that makes the 42S display 42.4242424242, assuming the display mode is STD or at least FIX 10. Simply keying the number in would require 13 keystrokes, so only solutions up to 12 keystrokes would count. I have found a 7keystroke sequence which has the additional advantage to be almost universal: if your calculator of choice is the HP41 you'd be able to use the same number of keystrokes to display 41.41414141 on it. And so to display 15.15151515 on your 15C, and 12.12121212 on your 12C, and so on.
A variation would be considering the calculator in its initial poweron state. In the case of the HP41 it defaults to FIX 4. So we'd like to display 41.4141 instead as shift FIX 9 would require three more keystrokes, which would spoil the fun. Of course displaying 41.4141 would require at least 8 keystrokes (ENTER is needed to hide the cursor). Interesting solutions should have 7 keystrokes at most. For instance, the 5keystroke sequence 2 SQRT 40 +would be a nice solution if it returned 41.4141 rather than 41.4142.
I came across the more general solution in less than ten minutes, which makes me guess this is a very easy challenge after all (or I was just lucky). The other solutions might be more interesting in case you're willing to try (so far I don't have any).
Best regards,
Gerson.
Posts: 3,229
Threads: 42
Joined: Jul 2006
Quote:
In case you're wondering about the title, this is kind of a little challenge: try to find the shortest RPN keystroke sequence that makes the 42S display 42.4242424242, assuming the display mode is STD or at least FIX 10.
.99 1/x 42 *
is seven keystrokes on a HP42S. It also generalises to other calculators as mentinoed.
 Pauli
Posts: 2,761
Threads: 100
Joined: Jul 2005
Congratulations! Really easy, isn't it?
Indeed, it can be solved in less than one minute, as I had just checked:
x = 42.4242...
100 * x = 4242.4242...

99 * x = 4242  42
99 * x = 4200
x = 4200/99
x = 42/.99
x = 1/.99 * 42
As I said, the second part should be more interesting for some models.
Best regards,
Gerson.
Posts: 3,229
Threads: 42
Joined: Jul 2006
I didn't attack it quite that way. I knew 1/9 and 1/11 and similar had "interesting" decimal expansions so I typed in 1.0101010101... and pressed 1/x.
 Pauli
Posts: 2,761
Threads: 100
Joined: Jul 2005
Contrary to what I thought some particular cases don't present any trouble at all:
10C: .099 1/x (5 keystrokes)
11C: .09 1/x (4 keystrokes)
15C: .066 1/x (5 keystrokes)
and so on...
Edited: 18 Sept 2006, 12:31 a.m.
Posts: 35
Threads: 1
Joined: Jan 2007
It was not very difficult, but it was funny! Thanks for posting.
Posts: 2,761
Threads: 100
Joined: Jul 2005
I'm glad you liked it. But definitely that was not so funny...
The 1<>2 toggle problem was much better:
http://www.hpmuseum.org/cgisys/cgiwrap/hpmuseum/archv015.cgi?read=74095
Posts: 1,193
Threads: 43
Joined: Jul 2005
Just a variant ...
1
Enter
%

1/x
*
Edited: 18 Sept 2006, 11:58 p.m.
Posts: 2,761
Threads: 100
Joined: Jul 2005
Really interesting!
I have also liked very much your general solution to Paul Dale's overflow challenge.
Best regards,
Gerson.
Posts: 1,193
Threads: 43
Joined: Jul 2005
Thanks, Gerson!
I appreciate your feedback very much.