退休广告文案人员罗伯特·吉尔伯特在1986年左右发明了一款名为Pago Pago的纵横字谜游戏[1]。据其子乔纳森的表述，这款谜题被设计为"莫比乌斯环"——一个"无限纵横字谜"，具有没有开始和结束的特点[1]。
根据数学家马丁·加德纳的定义，莫比乌斯环是拓扑学中的一种"非定向"表面，在这样的表面上，镜像不对称的物体绕行一周后会改变其对称性[1]。在这种复杂的几何结构上设计纵横字谜面临独特的挑战。为了实现莫比乌斯环纵横字谜的可行性，设计者需要利用具有镜像对称特性的字母，包括O、X、L、W、E、H、I、C、U、D、A等[1]。通过计算机辅助搜索，三字词典中仅包含23对可镜像词汇，这严重限制了设计的灵活性[1]。
Robert Guilbert, a retired advertising copywriter, invented a crossword puzzle game called Pago Pago around 1986 that employed the mathematical structure of a Möbius strip [1]. According to his son Jonathan, the puzzle was designed as a "Möbius strip"—an "infinite crossword"—a puzzle with no beginning and end [1]. In topology, a Möbius strip is defined as a non-orientable surface on which mirror-asymmetric objects change their symmetry after traversing once around the surface [1].
Designing crosswords on such a non-orientable surface presents significant constraints. The letters available for use must retain their appearance when mirrored, limiting the usable alphabet to O, X, L, W, E, H, I, C, U, D, and A [1]. When researchers used computer-aided methods to search a three-letter word dictionary for mirror-symmetric word pairs, they found only 23 viable pairs [1].