Rob,
Another way to solve the same house number problem is the odometer verb:
odo =:#:i.@(*/)
3 9${3+odo 3#3
┌─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┐
│3 3 3│3 3 4│3 3 5│3 4 3│3 4 4│3 4 5│3 5 3│3 5 4│3 5 5│
├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
│4 3 3│4 3 4│4 3 5│4 4 3│4 4 4│4 4 5│4 5 3│4 5 4│4 5 5│
├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
│5 3 3│5 3 4│5 3 5│5 4 3│5 4 4│5 4 5│5 5 3│5 5 4│5 5 5│
└─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘
or,
3 9${(odo 3#3){3 4 5
┌─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┬─────┐
│3 3 3│3 3 4│3 3 5│3 4 3│3 4 4│3 4 5│3 5 3│3 5 4│3 5 5│
├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
│4 3 3│4 3 4│4 3 5│4 4 3│4 4 4│4 4 5│4 5 3│4 5 4│4 5 5│
├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
│5 3 3│5 3 4│5 3 5│5 4 3│5 4 4│5 4 5│5 5 3│5 5 4│5 5 5│
└─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┴─────┘
Skip Cave
Cave Consulting LLC
On Wed, May 20, 2020 at 1:30 AM 'Rob Hodgkinson' via Programming <
[email protected]> wrote:
> Skip, I was asked this just the other day by my son in Primary Math, it is
> a beautiful solution for this (common) math question.
>
> “How many different 3 digit house numbers can you produce if the hardware
> shop has no other supplies than unlimited quantities of 3’s, 4’s and 5’s
> and what are those numbers”
>
> A math/statistics person says “1st number any of 3 4 5, 2nd number any of
> 3 4 5, 3rd number any of 3 4 5” so there are 3 x 3 x 3 (or 27) house
> numbers.
>
> But to produce the list, the beauty of “catalogue” (as its name implies)
> is a very elegant solution to these types of problems.
>
> { 3 4 5;3 4 5;3 4 5
> ┌─────┬─────┬─────┐
> │3 3 3│3 3 4│3 3 5│
> ├─────┼─────┼─────┤
> │3 4 3│3 4 4│3 4 5│
> ├─────┼─────┼─────┤
> │3 5 3│3 5 4│3 5 5│
> └─────┴─────┴─────┘
>
> ┌─────┬─────┬─────┐
> │4 3 3│4 3 4│4 3 5│
> ├─────┼─────┼─────┤
> │4 4 3│4 4 4│4 4 5│
> ├─────┼─────┼─────┤
> │4 5 3│4 5 4│4 5 5│
> └─────┴─────┴─────┘
>
> ┌─────┬─────┬─────┐
> │5 3 3│5 3 4│5 3 5│
> ├─────┼─────┼─────┤
> │5 4 3│5 4 4│5 4 5│
> ├─────┼─────┼─────┤
> │5 5 3│5 5 4│5 5 5│
> └─────┴─────┴─────┘
>
> $,{ 3 4 5;3 4 5;3 4 5
> 27
>
> > On 20 May 2020, at 4:08 pm, Skip Cave <[email protected]> wrote:
> >
> > Harvey,
> >
> > ...
> > If not, you get a very different result:
> >
> > 1 2 3;4 5 6;7 8 9
> >
> > ┌─────┬─────┬─────┐
> >
> > │1 2 3│4 5 6│7 8 9│
> >
> > └─────┴─────┴─────┘
> >
> > {1 2 3;4 5 6;7 8 9
> >
> > ┌─────┬─────┬─────┐
> >
> > │1 4 7│1 4 8│1 4 9│
> >
> > ├─────┼─────┼─────┤
> >
> > │1 5 7│1 5 8│1 5 9│
> >
> > ├─────┼─────┼─────┤
> >
> > │1 6 7│1 6 8│1 6 9│
> >
> > └─────┴─────┴─────┘
> >
> >
> > ┌─────┬─────┬─────┐
> >
> > │2 4 7│2 4 8│2 4 9│
> >
> > ├─────┼─────┼─────┤
> >
> > │2 5 7│2 5 8│2 5 9│
> >
> > ├─────┼─────┼─────┤
> >
> > │2 6 7│2 6 8│2 6 9│
> >
> > └─────┴─────┴─────┘
> >
> > ┌─────┬─────┬─────┐
> >
> > │3 4 7│3 4 8│3 4 9│
> >
> > ├─────┼─────┼─────┤
> >
> > │3 5 7│3 5 8│3 5 9│
> >
> > ├─────┼─────┼─────┤
> >
> > │3 6 7│3 6 8│3 6 9│
> >
> > └─────┴─────┴─────┘
> >
> >
> > Skip Cave
> > Consulting LLC
> >
> >
> > On Mon, May 18, 2020 at 3:38 AM HH PackRat <[email protected]> wrote:
> >
> >> On 5/17/20, HH PackRat <[email protected]> wrote:
> >>> I need to convert the following list of 5 (in reality, far more)
> >>> 11-character dates: ...
> >>> to a list of 5 boxed dates: ...
> >>
> >> Many THANK YOU's to those who responded! As usual with J, there's
> >> often more than one way to accomplish something--in this case, 5
> >> completely different ways that I can choose to add to my personal J
> >> vocabulary.
> >>
> >> The shortest was Skip Cave's response, but, Skip, I have a question
> >> about how/why yours works. When I read the Vocabulary and NuVoc to
> >> see how and why this works, I could not figure out how I would even
> >> think to use "{" (catalogue) based on the information in those two
> >> sources. The NuVoc definition/description is "Combines ITEMS from the
> >> ATOMS inside a BOXED LIST to form a catalogue." My original list was
> >> NOT boxed, so that description would automatically dismiss my example
> >> from using "{". Can you please clarify why "{" can be used to box an
> >> unboxed list?
> >>
> >> And, by the way, in my programming, I like to do things small step by
> >> small step so that I can be sure everything works correctly at each
> >> point. My original goal in this case was to get the unboxed list
> >> first boxed in the correct manner and then transpose it from a column
> >> to a row. (It's part of stock market data from a particular vendor
> >> which is out of "standard" order and format.) Three of the five
> >> responses did both aspects (box and transpose) in a single
> >> command--for which I am quite grateful. It showed me again how
> >> amazing J is!
> >>
> >> Harvey
> >> ----------------------------------------------------------------------
> >> For information about J forums see http://www.jsoftware.com/forums.htm
> >>
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
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