In a 24-space grid (4 columns × 6 rows or the signature 2-4-6-6-4-2 24-tile shape), sliding a tile horizontally changes the permutation inversion count by 0, while sliding vertically across a 4-column row jumps over 3 tiles—changing the inversion count by ±1 or ±3 (always odd) while changing the empty slot's row distance by ±1. Thus, (Inversions + Blank Row Distance) mod 2 is a strict mathematical invariant!
Tilting the 24-slot frame onto its diagonal axis breaks habitual horizontal reading order and recruits mental rotation alongside sequential planning—turning a familiar wooden slider into a deep spatial workout.
As showcased on the Twisted23 Lounge, an alternative to sliding a numbered tile into the empty slot is flipping a 3D-in-2D die across the frame—combining sliding-tile parity with the 24-state cube rotation group!
l
In sans-serif fonts, lowercase l (ASCII 108), uppercase I (ASCII 73), and numeral 1 (ASCII 49) look nearly identical. On Linux servers (Apache/Bluehost), URLs after the / are strictly case-sensitive—so we standardize on CameLcase (/LearningLab, SLog, FlippingDice, TopHat).
Every LearningLab in the Twisted23 Parlour stamps events using the 38-character alphabet (0-9, A-Z, |, ^—capital L only, zero lowercase ls!) counting seconds since March 18, 2020:
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