I don't understand the "number of different possible arrangements after N divisions".
If you have 4 rows, and you place the A in each row, the outcome will have 4 different arrangement regardless of how many divisions follow.
For C(2), I get 4 arrangements if first amoeba is placed in first column (see drawing).
What am I not getting?
Problem 762
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Problem 762
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Re: Problem 762
Two things:
So the first amoeba is in the bottomleft corner.Originally there is only one amoeba in the square (0,0).
A division is a division of a single amoeba, not the division of an entire generation. When an amoebe splits, it disappears leaving two new amoebas in the next column, so each division increases the number of amoebas by one. So for N=2 there will be three amoebas at the end, one in column 1 and two in column 2. There is no fixed order in which the amoebas split, and some may never split.After N divisions there will be N+1 amoebas arranged in the grid.
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Re: Problem 762
Oh, ok thanks  so if I understand you correctly, these would be the 2 arrangements after C(2)...
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 neverforget
 Posts: 46
 Joined: Sat Sep 16, 2006 10:10 pm
Re: Problem 762
Yes, though keep in mind that the grid continues to the right (only the height is constrained to 4 cells) and the individual amoebas are indistinguishable.