Problems & Puzzles: Puzzles
Puzzle 230. Primes and a tower of cubes
For those that found a kind of difficult the previous puzzle (229) maybe will find this new puzzle more affordable.
Here you are invited to allocate the numbers from 1 to N, in the N nodes of a tower of C cubes, such that the sum of the numbers of the two nodes at the extreme of each edge (horizontal and vertical) is a prime number.
Evidently in a tower like this, N = 8 + 4(C-1) and the number of edges E is E = 12 + 8(C-1). E is also the number of prime-sums formed in the process of allocation.
Example. For C= 10, N = 44, E = 84 (*)
1) Find the smallest
tower (the smallest C) that has solution.
Giovanni Resta solved this puzzle completely:
He also sent the solutions for C=20, 50 & 100 (too large to be exposed explicitly here)