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The ants from this puzzle have been placed into a new arena: a cross-shaped hallway with a pillar (black square) in the centre and four statues (numbered 1-4) set symmetrically. enter image description here

The ants, like last time, start off by trying to move East. If they encounter a boundary, the central pillar, a statue, or a cell they've already visited they turn to their left (if heading East, they turn North, if heading North they turn to the West, etc.) seeking a free direction to walk. They always move as far as they can in their chosen direction. When they cannot move anymore, they stop. As the arena is presented, it is (relatively) easy to find an ant-trail that covers all the squares and ends adjacent to the ant's starting square. So your task is:

Move one statue to a new position and identify a starting cell for the ant so that the ant covers all the free cells on its walk and does not return to the start of its walk.

I believe there is only one solution modulo rotational symmetry.

EDIT: ...and I'm wrong; there are at least two since JMP found one I didn't!

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  • $\begingroup$ So this time they don't try turning right if left doesn't work? $\endgroup$
    – Jaap Scherphuis
    Commented Dec 5, 2019 at 11:04
  • $\begingroup$ @Jaap not exactly: in both cases they always keep turning left until they find a direction to move, or they find there are none. However, if forwards is blocked and it's not the very first move, then backwards is also always blocked, so it has the effect of "turn left; if that fails try turning right from your original heading". Whichever is easier for you to work with $\endgroup$
    – user40528
    Commented Dec 5, 2019 at 11:06

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antz2

Start at the star and finish at the red circle.

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  • $\begingroup$ that's a good solution... and now I know that there is actually more than one solution, even taking rotational symmetry into account, and neither me nor my tester found this one! $\endgroup$
    – user40528
    Commented Dec 5, 2019 at 11:34

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