Teaching LinkedIn Queens #818: start with region scans on this 7×7 board. 7 regions, sizes 1–19. Walk students through 7 placements ending at R1C4, R2C2, R3C5, R4C7, R5C3, R6C6, R7C1.
Board spotlight: Several color regions span only a few cells — scan those regions first because they often force a queen into a single row or column. Region sizes range from 1 to 19 cells — smaller regions often pin a queen to a single row intersection.
Lesson step 1: show why R1C4 is forced. Row 1, column 4 is the forced queen once region 1, row, column, and touch rules are applied together. Ask: which rows/columns/regions are now closed?
Lesson step 2: show why R2C2 is forced. Region 3 only touches row 2 once on this board, so its queen must land at column 2. Ask: which rows/columns/regions are now closed?
Lesson step 3: show why R3C5 is forced. Row 3, column 5 is the forced queen once region 2, row, column, and touch rules are applied together. Ask: which rows/columns/regions are now closed?
Lesson step 4: show why R4C7 is forced. Region 6 only touches row 4 once on this board, so its queen must land at column 7. Ask: which rows/columns/regions are now closed?
Lesson step 5: show why R5C3 is forced. Row 5, column 3 is the forced queen once region 4, row, column, and touch rules are applied together. Ask: which rows/columns/regions are now closed?
Lesson step 6: show why R6C6 is forced. Region 7 only touches row 6 once on this board, so its queen must land at column 6. Ask: which rows/columns/regions are now closed?
Lesson step 7: show why R7C1 is forced. After eliminations, row 7 has one legal square left — column 1. Ask: which rows/columns/regions are now closed?
Recap: 7 queens, 7 regions, one solution path. Replay using region-first scanning.