Vertex labeling of a half-cube to induce face labels in arithmetic progression

Jyotirmoy Sarkar ()
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Jyotirmoy Sarkar: Indiana University-Purdue University Indianapolis

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 3, 593-608

Abstract: Abstract A plane, passing through the center and orthogonal to a diagonal, slices a cube into two identical halves each having three triangles, three pentagons and a hexagon. If you label the ten vertices of a half-cube with numbers, then each face is said to receive an induced face label given by the sum of all vertices around it. Label the ten vertices of a half-cube with digits 0 through 9 so that the induced labels of the three triangles and the three pentagons constitute six consecutive multiples of a fixed number, or more generally six numbers in arithmetic progression.

Keywords: Puzzle; Solution; Rotation; Reflection; Permutation; Greatest common divisor; 05C78 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00151-3

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