Cubic Diagonals and Edges (Posted on 2009-04-30)

Eg, diagonals:
                    A + Q = N + E = C + O ...(etc)
and edge cubes:     A + B + C = C + E + H = F + G + H ...etc,
                or (A + B + C) ±1 = C + E + H
                                  = F + G + H ....(etc) 

	Submitted by brianjn
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Solution:	(Hide)
It should be apparent that the diagonal sums are 21, 1+20, 2+19 .... Assigning unique values to the letters of the map and summing the 12 edges yields an average of 31.5. Since the edges sums are to be no more than one different from any other we require edges of 31 and 32. This occurs six (6) times with 31 and 32 being diagonally opposite. My value table was: A B C D E F G H I J K L M N O P Q R S T 10 19 3 16 20 6 17 8 9 7 12 14 13 1 18 2 11 5 15 4 My edge sums, and subsequent pairings were formed from: ABC 32 OPQ 31 ADF 32 QRS 31 CEH 31 MNO 32 FGH 31 MTS 32 FJO 31 CLS 32 AIM 32 HKQ 31 10 19 3 16   20 6 17 8 10 16 6 9   7 13 1 18 6 17 8 7   12 18 2 11 8 20 3 12   14 11 5 15 3 19 10 14   9 15 4 13 18 2 11 1   5 13 4 15 Realising that there would be multiple solutions I thought that I had assigned a specific value to A to limit such a range. However that has not been the case. Although this is my one solution, Charlie again has given us a comprehensive range. My comments above however do give a short summary of the nature of the problem.

	Subject	Author	Date
	Puzzle Answer	K Sengupta	2024-01-13 21:33:54
	re(2): computer solutions	Charlie	2009-05-03 12:13:31
	re: computer solutions	brianjn	2009-05-03 10:31:15
	re: computer solutions--the program	Charlie	2009-05-01 12:02:43
	computer solutions	Charlie	2009-05-01 11:59:18
	Restraint	brianjn	2009-05-01 10:09:41