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Amoebas escaping the prison

Puzzling Asked on February 28, 2021

There is an infinite grid of squares.

In one of the squares, there lives an amoeba (marked as a circle in the following pictures).

Amoebas cannot move, but they can perform their unique action: an amoeba can split itself into two amoebas, which are identical to the original one, and each will occupy a square that is (orthogonally) adjacent to the original square.

Since every square can only accommodate one amoeba, a splitting can only happen when the amoeba has at least two empty adjacent squares (if there are more than two, then it can choose freely to which squares to split). Also, two amoebas should not split simultaneously, so that no conflict should occur.

On the grid, there is a region called "the prison" (painted grey in the following pictures). The aim is to let the amoebas escape the prison, i.e. to reach a status that no amoeba is in the prison.


Question 1: Help the amoeba escape the following "cross" prison.

q1


Question 2: Help the amoeba escape the following "twisted cross" prison.

q2


Question 3: What about the following "octagon" prison, which is the combination of the previous two?

q3


Note:

  • The solutions are obviously not unique, as one may continue splitting after escaping from the prison. Thus in principle, you should try to use as few splittings as possible.

  • Click the pictures for larger versions. Although the picture only shows an $11 times 11$ part of the grid, the actual grid is infinitely large and the solution may extend to outside.

2 Answers

Here is the first part solution (Question 1):

Here is the second part solution (Question 2):

Answered by Oray on February 28, 2021

My solution for question 2

Answered by Retudin on February 28, 2021

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