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What you see above is a tool to reorder the pages of a PDF file, into the order as described by Brent Yorgey here (called “Möbius double-sided printing” here). Basically, it reorders the n pages [1, 2, …, n] of a PDF file into the order [1, m+1, 2, m+2, 3, m+3, … m, 2m], where m = ⌈n/2⌉, and the final page 2m is omitted if it doesn't exist (i.e., if n is odd).
To use this tool, just upload a PDF file above, then click on the link to download a new PDF file with reordered pages.