# Floor tiles

Acolyte
Posers and Puzzles 23 Jul '04 08:29
1. Acolyte
Now With Added BA
23 Jul '04 08:292 edits
There is a square room with a chessboard-patterned floor. The walls and ceiling are completely smooth and featureless except for in two places: behind the White Queen's square, there is a door, and set in the wall next to the Black Queen's square there is a safe containing an extremely valuable chess set made with jewels and precious metals.

The tiles are very large, so you can only make King's moves. When you place your full weight on a tile, it and all tiles with which it shares a side flip from white to black or from black to white. However, walking or jumping on the same tile will not cause it to flip repeatedly - if you want to flip it again you have to activate another tile first.

Both the door and the safe are quite small and can only be reached from the respective Queen's squares. They are also both unopenable and unmoveable, except when the tiles form a perfect chessboard pattern, as they do initially. You start standing outside the room, by the door. You don't have any tools, implements or accomplices to help you.

You want to take the chess set out of the room - but how?
2. TheMaster37
Kupikupopo!
23 Jul '04 17:03
Does the floor as given represent the perfect chess floor, or does the mirrored image (eg with a different colour in the bottom left square) count as a perfect chess floor as well.

I assume you cannot walk around the room and blast a hole in the back of the safe...

Nasty problem. You can't even walk back the way you came...
3. Acolyte
Now With Added BA
23 Jul '04 19:302 edits
Originally posted by TheMaster37
Does the floor as given represent the perfect chess floor, or does the mirrored image (eg with a different colour in the bottom left square) count as a perfect chess floor as well.

I assume you cannot walk around the room and blast a ...[text shortened]... ..

Nasty problem. You can't even walk back the way you came...
I'll say a mirror image is not allowed, as I think you're barking up the wrong tree there. This isn't a lateral thinking puzzle, you just have to move over the squares in the right way.

I can do it in 64 moves, in a way that's quite easy to describe (it effectively splits into 4 stages). I don't know if there's a quicker way to do it, but I'd be interested to see either that or a proof that 64 is the minimum number of moves.
4. 23 Jul '04 21:21
Originally posted by Acolyte
I'll say a mirror image is not allowed, as I think you're barking up the wrong tree there. This isn't a lateral thinking puzzle, you just have to move over the squares in the right way.

I can do it in 64 moves, in a way that's quite easy to describe (it effectively splits into 4 stages). I don't know if there's a quicker way to do it, but I'd be interested to see either that or a proof that 64 is the minimum number of moves.
Haven't thought this through properly, but would I be right in thinking that if I stand on a square (causing a flip) then move to an adjacent square (a 2nd flip), back to the original square (cancelling flip 1) and then onto my adjacent square again (cancelling flip 2), I'll have an unchanged pattern? In which case it takes me 4 moves to move a 2 squares. That would get me to the safe in 16 moves.... then I need to get back. The problem with my idea is I can only move 2 squares at a time and there are only 7 on the direct path back to the door (excluding the one I'm on). Essentially I'm stuck on the white squares... but I can get to any white square pretty easily. I think changing from one colour to the other must be exceedingly convoluted... I'll give it some more thought.

Mike
5. Acolyte
Now With Added BA
23 Jul '04 21:322 edits
Originally posted by mikenay
Haven't thought this through properly, but would I be right in thinking that if I stand on a square (causing a flip) then move to an adjacent square (a 2nd flip), back to the original square (cancelling flip 1) and then onto my adjacent sq ...[text shortened]... exceedingly convoluted... I'll give it some more thought.

Mike
You're on the right track. I've just realised I can do it in 32 moves - remember, I did say you could make King's moves.
6. TheMaster37
Kupikupopo!
24 Jul '04 10:14
My approach was more into thinking i'd need to flip the entire board over, making back tiles white and white tiles black. I hadn't thought of Mike's approach yet (stupid really there is a game i play sometimes wich relies on this principle).
7. 27 Jul '04 19:53
door -&gt; D1,D2,D1,D2,D3,D4,D3,D4,D5,D6,D5,D6,D7,D8,D7,D8 -&gt; safe -&gt; {same moves backwards} -&gt; door
8. Acolyte
Now With Added BA
27 Jul '04 19:59
Originally posted by iamatiger
door -> D1,D2,D1,D2,D3,D4,D3,D4,D5,D6,D5,D6,D7,D8,D7,D8 -> safe -> {same moves backwards} -> door
The safe is in the wall, and you can't step inside it. You get the chess set, but the door is locked.
9. 27 Jul '04 20:22
Originally posted by Acolyte
The safe is in the wall, and you can't step inside it. You get the chess set, but the door is locked.
ok, didn't realise that it wasn't a room safe ðŸ™‚

door -&gt; D1,D2,D1,D2,D3,D4,D3,D4,D5,D6,D5,D6,D7,{D8,D7,D8 (get jewels),E7,D7,E7}, moves outside brackets backwards -&gt; door
10. psychopath42
Green Slime
02 Aug '04 00:051 edit
Originally posted by iamatiger
ok, didn't realise that it wasn't a room safe ðŸ™‚

door -> D1,D2,D1,D2,D3,D4,D3,D4,D5,D6,D5,D6,D7,{D8,D7,D8 (get jewels),E7,D7,E7}, moves outside brackets backwards -> door
oops, posted by accident, carry on