The good news: 2 new problems yesterday after a lull for several months.
The bad news (for me): I don't understand them!
... which is often the case, but here, I don't even get the Mickey
Mouse case.
It's not done to "spoil" these problems for others, but I don't think
it's cheating to
invite an explanation for how C(2) = 2 for problem 762. Once I
understand what they
want I can go on and (probably not) be able to solve it for myself.
As I mis-understand it, the starting position is (0,0) and there's only
one state at each generation.
Where does the multiplicity arise?
I should post my query in their Clarifications Forum, but don't fancy
being trolled there - much
better to be teased by fellow J(oker)s.
The original of problem 762 can be found here:
https://projecteuler.net/problem=762
Here's a copy, modified to non-graphics, roughly as pasted into my
proto-script:
... better in a fixed width font:
NB. Problem 762
NB. Consider a two dimensional grid of squares. The grid has 4 rows but
infinitely many columns.
NB. An amoeba in square (x, y) can divide itself into two amoebas to
occupy the squares (x+1,y) and
NB. (x+1,4|y+1), provided these squares are empty.
NB. The following diagrams show two cases of an amoeba placed in square
A of each grid. When it divides, it is
NB. replaced with two amoebas, one at each of the squares marked with B:
NB. (origin at J matrix index 3 0)
NB. ('abb' (3 2 3, each 0 1 1) } 4 6 $ '.'),.(4 4$' '),. 'abb' (0 0
3, each 3 4 4) } 4 6 $ '.'
NB. ...... ...ab.
NB. ...... ......
NB. .b.... ......
NB. ab.... ....b.
NB. Originally there is only one amoeba in the square (0, 0). After N
divisions there will be N+1 amoebas
NB. arranged in the grid. An arrangement may be reached in several
different ways but it is only counted once.
NB. Let C(N) be the number of different possible arrangements after N
divisions.
NB. For example, C(2) = 2, C(10) = 1301, C(20)=5895236 and the last nine
digits of C(100) are 125923036.
NB. Find C(100,000), enter the last nine digits as your answer.
One for Joseph Turco, perhaps; and thanks for any, non-spoiler, tips!
Mike
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