### Checkerboard

Posted:

**September 14th, 2017, 2:18 pm**There have been a short discussion about the checkerboard (the board, not the chess pieces):

http://snkhan.co.uk/forum/viewtopic.php ... ard#p28670

but this post concerns a more general challenge: folding the nxn checkerboard from a single square sheet of paper with one color per face. Additionnaly, the question is: what is the optimal design (i.e. the smallest initial square for the same folded design)?

An old (2000) upper bound on the paper size has been stated in

https://hal.archives-ouvertes.fr/hal-01380815

It has been outperformed (2009) in

https://dspace.mit.edu/openaccess-disse ... 21.1/62156

but only for n > 16. Since then, there have been several effectively folded models of the expected optimal chessboard (n=8), but I have not seen real models folded for a larger n.

So, here is my latest attempt: the 11x11 checkerboard

from a 60x60 paper (half-folded to feel the complexity).

The design principle is not new, and is described in

https://arxiv.org/abs/1510.07499

but the real physical folding may well be.

So, the question is:

the effective folding of the optimal 11x11 checkerboard (i.e. from the smallest initial square of paper - not proved but strongly suspected), is it a world record??

http://snkhan.co.uk/forum/viewtopic.php ... ard#p28670

but this post concerns a more general challenge: folding the nxn checkerboard from a single square sheet of paper with one color per face. Additionnaly, the question is: what is the optimal design (i.e. the smallest initial square for the same folded design)?

An old (2000) upper bound on the paper size has been stated in

https://hal.archives-ouvertes.fr/hal-01380815

It has been outperformed (2009) in

https://dspace.mit.edu/openaccess-disse ... 21.1/62156

but only for n > 16. Since then, there have been several effectively folded models of the expected optimal chessboard (n=8), but I have not seen real models folded for a larger n.

So, here is my latest attempt: the 11x11 checkerboard

from a 60x60 paper (half-folded to feel the complexity).

The design principle is not new, and is described in

https://arxiv.org/abs/1510.07499

but the real physical folding may well be.

So, the question is:

the effective folding of the optimal 11x11 checkerboard (i.e. from the smallest initial square of paper - not proved but strongly suspected), is it a world record??