Add Mathematica notebook solving 27-matchstick puzzle (88 ÷ 31 = 14)

[Copilot]

The equation 88 ÷ 31 = 14 is displayed with 27 matchsticks using 7-segment digit style. The equation is incorrect (88/31 ≈ 2.84); the task is to rearrange matchsticks—no additions or removals—to form a valid equation.

Approach

• Segment counts modeled as an Association: 0→6, 1→2, 2→5, 3→5, 4→4, 5→5, 6→6, 7→3, 8→7, 9→6
• Search space: all XX ÷ YY = ZZ with leading zeros permitted per digit slot, total segment count = 27
• Minimum physical moves computed per candidate: sum of segment increases across fixed digit positions (equals segments to be removed, since total is conserved)

Result

56 ÷ 04 = 14 — requires only 3 matchstick moves, the minimum over all valid solutions:

Position	Original	New	Δ segments
Tens of dividend	8 (7)	5 (5)	−2
Units of dividend	8 (7)	6 (6)	−1
Tens of divisor	3 (5)	0 (6)	+1
Units of divisor	1 (2)	4 (4)	+2
Result 14	—	unchanged	0

Segment totals: 11 + 10 + 6 = 27 ✓, and 56 / 4 = 14 ✓.

Notebook: cerillos.nb

• Digit segment table and helper functions (cer, cer2)
• Original equation verification (27 matchsticks confirmed)
• Brute-force Reap/Sow search over all 2-digit × 2-digit candidates
• Results table sorted by minimum physical moves, optimal rows highlighted
• Detailed per-digit change breakdown for the optimal solution

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