L2 · Find the error; create your own variation
“I can audit someone else's puzzle work like a referee: verify a claimed solution move by move, find illegal moves and impossible claims, and explain the error precisely. I can also design a fair variation of a puzzle - changing exactly one rule, piece or goal - and describe the strategy the variation calls for, including predicting its new solution counts.”
Worked example 1 - the count catches it: a claimed tiling covers a 6 x 4 board (24 unit squares) "using 5 pentominoes." Count first: 5 pentominoes cover 5 x 5 = 25 squares, which is not 24. The claim is dead before a single placement is examined - eliminate it and move on. Worked example 2 - the illegal move: a Hanoi move list contains "...4) Large -> Spare, landing on Small." Illegal: a larger disc may never sit on a smaller one. One illegal move invalidates the whole claimed solution, wherever it occurs. Worked example 3 - the piece that must flip: the tangram parallelogram is the one piece whose mirror image cannot be matched by rotating it in the plane - its slant leans the "wrong" way. In several silhouettes it fits only when flipped OVER (turned out of the plane). A solver who only rotates it will wrongly conclude the silhouette is impossible. Say it plainly: refereeing is a skill with an order - count the totals, check every move's legality, and only then judge the placements.
The counting check is run FIRST because...
A claim: tile a 3 x 6 board (18 squares) with pentominoes. Verdict, with reason? -> Impossible - 18 is not a multiple of 5, so no whole number of 5-square pieces can cover it exactly
"To audit a claimed solution: 1) check the ___ totals; 2) check every move is ___; 3) trace the ___ position of every piece." -> Area/count; legal; final
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.