Teaching LinkedIn Queens #798: start with region scans on this 7×7 board. 7 regions, sizes 1–27. Walk students through 7 placements ending at R1C1, R2C3, R3C6, R4C4, R5C2, R6C7, R7C5.
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 27 cells — smaller regions often pin a queen to a single row intersection.
Lesson step 1: show why R1C1 is forced. Region 1 only touches row 1 once on this board, so its queen must land at column 1. Ask: which rows/columns/regions are now closed?
Lesson step 2: show why R2C3 is forced. Region 4 only touches row 2 once on this board, so its queen must land at column 3. Ask: which rows/columns/regions are now closed?
Lesson step 3: show why R3C6 is forced. Row 3, column 6 is the forced queen once region 5, row, column, and touch rules are applied together. Ask: which rows/columns/regions are now closed?
Lesson step 4: show why R4C4 is forced. Region 6 only touches row 4 once on this board, so its queen must land at column 4. Ask: which rows/columns/regions are now closed?
Lesson step 5: show why R5C2 is forced. Row 5, column 2 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 6: show why R6C7 is forced. Row 6, column 7 is the forced queen once region 3, row, column, and touch rules are applied together. Ask: which rows/columns/regions are now closed?
Lesson step 7: show why R7C5 is forced. After eliminations, row 7 has one legal square left — column 5. Ask: which rows/columns/regions are now closed?
Recap: 7 queens, 7 regions, one solution path. Replay using region-first scanning.