# 5×5 illegal parity - how could I move the centerpieces to fix it?

My cube was dropped (kids uugh) and only three center pieces fell out (red blue and yellow). I put them back where I thought they should be, and then solved the cube.

The end result is this weird parity :( (all non-visible pieces are properly solved).

Instead of taking apart the entire cube, I'd rather just relocate those centerpieces (and then glue them in). Does anyone know how to correctly relocate them?

• Do you want to take apart your cube again? Oct 19, 2022 at 12:50
• Absolutely not! I’d like to relocate only the center pieces and then solve it regularly. But I don’t know where to locate each centerpiece. Oct 19, 2022 at 15:18
• The point is, you will have to disassemble it a bit to fix it. And that means somehow it has been partially disassembled before. Oct 19, 2022 at 20:45
• Were they just the center caps? Or were they some of the pieces in the center ring? Oct 20, 2022 at 14:17
• That's what I was told..... I'm beginning to doubt them... Oct 20, 2022 at 19:44

You can offset any four centers on the same band a quarter turn. For example, the red center is blue, blue is orange, orange is green, and green is red. But symmetry means there are six equally valid methods to fix your cube.

This parity shows up a lot on the void cube.

EDIT: Added image; Both of the twisty puzzles are still in a valid state while mimicking the parity issue presented. You can rearrange your centers to copy the left puzzle to resolve the parity. The green face has the orange cap and the red face has the green cap.

Now, how you managed it with three caps, I'm really not sure. I think the cube was broken already or your kids tried to fix it without you noticing.

• That is the answer! wonderful!! thanks. I must have returned the third cap to the correct spot. I can finally sleep :) Oct 20, 2022 at 19:41
• @AnnaRosenberg I had to move four different caps. On the backside, the green face has the orange cap and the red face has the green cap. Are you sure you knocked out only three? Oct 20, 2022 at 20:53
• That would be good to add that to the explanation. One mo~ Oct 20, 2022 at 21:18
• I'm not at all sure it was only three. You nailed it!! cube solved in no time. thanks Oct 21, 2022 at 8:59

Assuming only true centre pieces fell out, your parity error can be fixed by cycling a ring of four centres by 90°, then re-solving. This is equivalent to a 4-cycle of edges, which together with the observed corner swap gives an even, i.e. solvable permutation.

With three centres falling out you must have put one back in the correct place.

• Is there any way to avoid taking it apart? I've never done that Oct 19, 2022 at 15:21
• The truth is, I'm new to cubing. I have no idea how this happened (I do know that some centerpieces had fallen out) and I would like help getting it solved… Oct 19, 2022 at 15:25
• @AnnaRosenberg Sorry, this is a proven fact. Oct 19, 2022 at 19:47
• @AnnaRosenberg yea, Parcly is trying to say that this position can't be reached even if you replace the centerpieces. So, probably, give this to the kids and wait for them to drop it again? :) Oct 20, 2022 at 14:49