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Order-3 magic cube
42
Magic constant of a normal order-3 magic cube. M₃(3) = 42.
A magic cube stacks numbers so every straight line through the block adds to the same total. The smallest one that works uses 1 through 27. Those lines add to 42. Order-3 perfect cubes do not exist. Semiperfect, or Andrews, cubes do: rows, columns, pillars, and the four space diagonals.
What it supports
An exact combinatorial constant. n(n³+1)/2 at n=3 is 42. OEIS A027441. MathWorld. Center cell 14. Opposite cells 28. Hendricks: four such cubes up to rotation and reflection. Hugel 1876.
What it does not
Not a perfect magic cube. Slice diagonals need not sum to 42. Not Catalan C₅. Not Adams. Not a measured 42 in space.
Calculation
M₃(n) = n(n³+1)/2. n = 3 → 3×28/2 = 42.
Normal magic cube. Consecutive integers 1 through 27.
ExactnessExact
Form42
Unitsum
Strengthhard
When1876