The row counts below four columns were the naive division, not what the board does

2026-08-25 17:21:20 -04:00
parent 820e8325a6
commit 128172d3a8
1 changed files with 8 additions and 3 deletions
@@ -13,9 +13,14 @@
 //   Powers of two, all the way down.
 //       Column counts are 8, 4, 2, 1 and every span is 1, 2, 4 or 8. That pairing is what makes
 //       the board tile with no holes at every width without a single hand-placed card: 32 span
-//       units divide into 8 columns as 4 rows, into 4 as 8 rows, into 2 as 16, into 1 as 32.
+//       units divide into 8 columns as 4 rows and into 4 as 8. A rung of 6 or 10 columns does
-//       A rung of 6 or 10 columns does not divide a span of 4, which is why the previous ladder
+//       not divide a span of 4, which is why the previous ladder needed a per-breakpoint
-//       needed a per-breakpoint override for every wide card and still left holes.
+//       override for every wide card and still left holes.
 //
 //       Below four columns the arithmetic stops being a division. Spans clamp to the column
 //       count, so a span-4 card contributes 2 at two columns and 1 at one, and the board is 13
 //       rows and then 18 rather than the 16 and 32 a naive division predicts. It still tiles
 //       without holes, for a different reason: a clamped card fills its row outright.
 //
 //   Breakpoints are arithmetic, not taste.
 //       A column count is viable exactly when the cards still fit: