MC: 4th power with no small digits
in [HP48]
|
Prev: (Sorry for the non french speaking peoples) Un logiciel de géométrie dynamique pour HP
Next: Dust inside 50g. How to clean? How to prevent?
From: Han on 25 Mar 2010 21:24 > It would *seem* that all integers raised to the 4th power contain at > least one digit less than 5. For example, 26 to the 4th power is > 456976, which contains a 4. However, there does exist a positive > integer X such that X^4 contains no digits less than 5. > I am starting to believe that it is possible to solve this problem completely using elementary number theory. Let's see what a few more days of proofs produce =)
From: Brian Walsh on 26 Mar 2010 02:49 On Mar 23, 8:23 pm, Joe Horn <joeh...(a)holyjoe.net> wrote: > > > Tumbolia, the place where hiccups go when they go away. ;-) > > > Uh, as I recall, one of the GEB dialogs refers to Tumbolia as the > > destination of lost / mismatched socks. Those two ingredients lead to > > a disquieting mental image... > > That's why getting a good sock in the mouth makes hiccups go away. > > -Joe- Ahmghnathkuhfthtwhn (removes sock from mouth) I'm gonna sock you for that one. *hic* Brian
From: stephen on 26 Mar 2010 19:05 Hi everyone, Can I just say that I love this? I just bought my first HP calculator a few months ago. Not used an RPN calculator before, though did do Forth programming earlier in my career so very familiar with the concept. I bought the HP48Gii which I know a lot of you will probably have a problem with, but I couldn't really afford or justify an HP50g, though I might buy one one day if I really use this one a lot. It's also the duff old HP48Gii with only 3xAAA and no USB port. Read several things saying this one had been superseded, but even HP's website now lists the model I have as current and doesn't mention a USB version. I happened upon this group while using google to search for the solution to a problem I had. What luck! Anyway, I managed to solve the MC, though my version of the program took just over an hour to run! :-D I really wasn't trying hard to optimise it, I just wanted to produce something and to try out some of the stuff I've learned since I bought the calculator. I also wanted to break the program down into manageable chunks so I used several routines to achieve what I wanted to do. I know this will probably affect how long it took significantly, but I'm really just doing this for fun and to learn, not to compete! :-) Here's what I did, if anyone is interested. Don't rip it all apart, but friendly comments very welcome! First I figured that I would want to work out how to check if one of these numbers matches the criterion of having no digits less than 5, and to do this I would want to treat each digit separately, so I thought it would be nice to separate the number out into a list of digits. My first routine takes a number from the stack, and returns to the stack the last digit along with the rest of the number ready for processing: GetD: << DUP 10 IDIV2 DROP SWAP 10 MOD >> e.g. 123 GetD returns 12 3 The next routine takes a list and a number, and returns the same list with the last digit of the number added, plus the rest of the number for processing: AddD << GetD ROT SWAP + SWAP >> e.g. { 1 } 23 returns {1, 2} 3 The next routine takes a number from the stack, and returns a list containing the digits of that number on the stack DList: << { } SWAP WHILE DUP 0 <> # ok, so really it's the proper not equals symbol! REPEAT AddD END DROP >> e.g. 12345 returns {1, 2, 3, 4, 5} The next routine tests if a number has any digits less than 5. I was thinking about how to do a foreach type thing and how I could write something to run a given routine on each element of a list and either AND or OR the results together. Then I remembered that I can do an operation on a list and it does it on each element. I really like this! DigL5: << DList 5 >= #LIST NOT >> # #LIST's # is really pi for product of #list. So then I did my main routine. I skipped doing 1, since I found that #LIST fails with one element. Seems kind of daft to me, surely it should just return that element, but never mind. << 2 -> X << WHILE X 4 ^ DigL5 REPEAT X 1 + DUP 'X' STO 4 DISP END X >> >> This returns the answer as Jim revealed above. The DISP stuff was just added so I can tell it is really doing something because it takes so long! I'll probably spend some time looking at how I can optimise it now. One obvious optimisation, now I've structured it so I can understand what's going on would be to get rid of some of these abstraction layers. Then I'll be able to, for example, abort checking a number when I first see a digit <5 rather than having to extract all the digits before I process any of them. Thanks very much Joe. That was a very entertaining diversion, and it's really helping me to get acquainted with this great machine. Hope I haven't bored everyone too rigid with all the detail! Stephen Blythe
From: Han on 27 Mar 2010 00:19 I think your program is great for someone who just recently started programming in RPL. Over time you will learn how to optimize your program as you discover how certain objects are handled by the calculator. Also, the more mathematics you know (about the problem), the more you can optimize your program. For example, is it necessary to actually create a list of all the digits prior to checking each digit? Perhaps within your subroutine that extracts each digit, you may as well test the digit too... and stop as soon as you find a "small" digit. You will eventually see that oftentimes, there is a lot of "checking" that is extraneous. Regarding what I just wrote, if you notice that the first digit is already "small", then is there any reason to check the remaining digits? Other things to try: consider turning a number into a character string, and search the digits that way (see the SUB command). You may find that extracting characters from a string requires less of the CPU than using integer division. Moreover, the effect you want can also be achieved with HEAD and TAIL (these are commands). Anyway, as Joe said from the outset -- the key is to have fun. Judging from your post, I think you've done just that! Good luck in your pursuit of understanding RPN, RPL, and the HP series of calculators! Han
From: Dave Hayden on 27 Mar 2010 09:59
On Mar 26, 7:05 pm, stephen <s...(a)urwick.co.uk> wrote: > Hi everyone, > I bought the HP48Gii which I know a lot of you will probably have a > problem with, but I couldn't really afford or justify an HP50g, though > I > might buy one one day if I really use this one a lot. > It's also the duff old HP48Gii with only 3xAAA and no USB port. Read > several things saying this one had been superseded, but even HP's > website now lists the model I have as current and doesn't mention a > USB > version. Personally, I think the 48gII is an excellent value. Check out HPUserEdit or Debug4x for programming. It's much easier to develop programs on a PC and then download them to the calculator when you're done. > Anyway, I managed to solve the MC, though my version of the program > took > just over an hour to run! :-D I think your post is an excellent example of how to break a program into manageable parts, so even though it might not be super fast, it's a great tutorial. Thanks for posting it. Dave |