2009/8/23 Andrew Nikitin <[email protected]>:
> ...
> One of my children showed some interest in programming.
> So I am trying to find a base of programming problems from very simple and 
> going up in complexity
> ...

I don't know whether the following two would be of interest to you, as using
any of them implies using a specific programming language, but anyway ...

Do you know of GeomLab (http://web2.comlab.ox.ac.uk/geomlab)?
It is a functional programming language having numbers and
pictures as primitive datatypes.  Although the language is
very small and simple, it can be used to teach/learn important,
non-trivial algorithmic techniques.  As the tutorial shows,
the level of difficulty of the problems to program in GeomLab
spans a suitably wide range, from very simple to really hard.

GeomLab's programming paradigm should be familiar and appealing
to a J programmer, and surely most of GeomLab can be expressed
in J (often in a number of interesting ways not possible in
GeomLab itself).

Another programming environment that might be of interest in
the context of learning to program from novice to wherever you
want is Elica (http://www.elica.net).  Elica is a Logo-like
language with a form of prototype-based OOP, rich 3D graphical
facilities and other attractive features.

Regards,
    Boyko
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