Problems & Puzzles:
entry 1156 of the always interesting
Claudio Meller, we generate the following extension:
Given a zero free number N
composed by D distinct digits, obtain all of his D! permutations.
Calculate the sum S of all of the D!(D!-1)/2 absolute differences between
each two permutations, and report N only if N divides S.
I have obtained the following solutions:
Q1. Obtain the
solutions for D=7, 8 & 9. (BTW, confirm that there are NO
solutions for D=2 & 5).
Q2. Is there a N prime solution or this
Contributions came from Giovanni Resta, Abhiram R Devesh and
& Vantieghem made the same contribution:
The only solution missing from the table of Puzzle 698 is, for
D=7, N=1943568 (S=37148697938880). No solutions for D=8 or D=9.