It's been a long time since I considered this problem, so prompted by seeing this question I was intrigued to discover more on V. Bálint's bound of $(501/500)^ 2.$

A quick search revealed Bálint's paper A Packing Problem and Geometrical Series. In this article it is only stated that with some patience one can pack the first 499 rectangles into the unit square. However, the main difficulty of the problem is to pack the larger rectangles and so it would have been nice to see a demonstration.

Bálint addresses the question in Two Packing Problems but I do not have easy access to this and so now I'm concerned that a similar claim, without a demonstration, may have been made in this paper too.

Please could someone with access to the paper lay my concern to rest?

I would very much like to have confidence in the later bound as its validity makes the problem yet more interesting. Can we get arbitrarily close to 1? I still see no good reason why this should be the case but it's a fascinating possibility that hints at the prospect of something quite deep going on.

It's been a long time since I considered this problem, so prompted by seeing this question I was intrigued to discover more on V. Bálint's bound of $(501/500)^ 2.$

A quick search revealed Bálint's paper A Packing Problem and Geometrical Series. In this article it is only stated that with some patience one can pack the first 499 rectangles into the unit square. However, the main difficulty of the problem is to pack the larger rectangles and so it would have been nice to see a demonstration.

Bálint addresses the question in Two Packing Problems but I do not have easy access to this and so now I'm concerned that a similar claim, without a demonstration, may have been made in this paper too.

Please could someone with access to the paper lay my concern to rest?

I would very much like to have confidence in the later bound as its validity makes the problem yet more interesting. Can we get arbitrarily close to 1? I still see no good reason why this should be the case but it's a fascinating possibility that hints at the prospect of something quite deep going on.

It's been a long time since I considered this problem, so prompted by seeing this question I was intrigued to discover more on V. Bálint's bound of $(501/500)^ 2.$

A quick search revealed Bálint's paper A Packing Problem and Geometrical Series. In this article it is only stated that with some patience one can pack the first 499 rectangles into the unit square. However, the main difficulty of the problem is to pack the larger rectangles and so it would have been nice to see a demonstration.

Bálint addresses the question in Two Packing Problems but I do not have easy access to this and so now I'm concerned that a similar claim, without a demonstration, may have been made in this paper too.

Please could someone with access to the paper lay my concern to rest?

I would very much like to have confidence in the later bound as its validity makes the problem yet more interesting. Can we get arbitrarily close to 1? I still see no good reason why this should be the case but it's a fascinating possibility that hints at the prospect of something quite deep going on.

It's been a long time since I considered this problem, so prompted by seeing this question I was intrigued to discover more on V. Bálint's bound of $(501/500)^ 2.$

A quick search revealed Bálint's paper A Packing Problem and Geometrical Series. In this article it is only stated that with some patience one can pack the first 499 rectangles into the unit square. However, the main difficulty of the problem is to pack the larger rectangles and so it would have been nice to see a demonstration.

Bálint addresses the question in Two Packing Problems but I do not have easy access to this and so now I'm concerned that a similar claim, without a demonstration, may have been made in this paper too.

Please could someone with access to the paper lay my concern to rest?

I would very much like to have confidence in the later bound as its validity makes the problem yet more interesting. Can we get arbitrarily close to 1? I still see no good reason why this should be the case but it's a fascinating possibility that hints at the prospect of something quite deep going on.