1. Playing With Fire
1.3
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Don’t Fence Me In
Apply all match rules. Same size and shape for all squares. Only find distinct solutions, ignore symmetrical solutions.
A Remove two matches, leave four squares
B Rearrange two matches, leave four squares Keep 5 squares, remove matches: C eight D six E four Keep 6 squares, remove matches: F three G four H five I six Keep 7 squares, remove matches: J four K three L two Keep 4 squares, remove matches: M eight
1.4
Orphans Away
These problems have orphaned matches, their solutions must not. Apply all match rules. All squares must have same size, shape.
A Move two matches, make five identical squares
B Move three matches, make three identical squares Detailed analysis starts on page 11
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C: Per square, identify which matches can be removed and still maintain an overall stable composite structure (no orphans). Remove [a]: [d] is orphaned as a result, and must also be removed. [1] is broken. [e] belongs to [1] and [2]. As long as [2] is not broken as well (do not remove any of [bif]), [e] will not be orphaned, and the composite structure will remain stable. Similarly, [h] belongs to [1] and [4] (adjacent squares sharing [h]). Now that [1] is broken (by removing [ad]), do not break [4] as well (do not remove any of [kol]). Remove [b]: [2] is broken. [e] still belongs to [1], [f] still belongs to [3], [i] still belongs to [5]. Remove [i]: [25] are broken (by shared [i]); remove orphan [b]. [e] (still belongs to [1]) and [f] (still belongs to [3]) are not orphaned. Similarly, [m] belongs to [6], [p] belongs to [8], [l] belongs to [4]. If you remove [i], you must remove [b] ([i] is dependent on [b]). Remove [b] without affecting [i] ([b] is independent of [i]). Remove [e]: [12] are broken. Remove [abd] to prevent orphans. Remove [ef]: [123] are broken ([12] share [e], [23] share [f]). Remove unstable [abcdg], and prevent orphans. Other matches/combinations are symmetrical versions of these. Only three distinct squares and their symmetrical versions: [1]: [3], [7], [9];
[2]: [4], [6], [8];
[5].
For a symmetrical figure, solutions would probably involve removing matches symmetrically. With what you now know, you have all the techniques to solve this group of problems. Fair warning though, analysis will take time and yield many solutions! There may be more solutions than those shown. Keep analyzing!
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Use tips, tricks, and techniques learned so far. Try (moving and/or removing) combinations of matches and sets of matches. Solutions come with trial and analysis (not error or randomness!) C1: A symmetrical solution, break alternate outer squares. C2: Break two adjacent outer squares. C3: Found with insight gained from C2. C4: A modified version of C3 (remove [beil], replace [cgjn]). C5: A modified version of C3 (remove [ux], replace [jn]). C6: Remove [rstuvwxb]. One row of squares is eliminated. C7: [1] (adjacent to [2], [4]) shares [e] with [2] and [h] with [4]. Remove [abdehk] (destroy [124]). Now remove [ux] (destroy [9]). Note: If you needed to keep four squares by removing eight matches (Problem M!), you would remove [nw] instead of [ux].