Cody

Problem 2652. Kurchan 5x5 - Optimal Score

Related to Problems 1646 and 2650, but bigger. Technically, all you need to do for this Cody problem is input a 5x5 matrix containing the numbers 1-25. However, your score will be the Kurchan value of the matrix, which is defined as the difference between the maximum and minimum of the products for the rows, columns, diagonals, and anti-diagonals of the matrix.

For example: Magic(5) is

    17    24     1     8    15
    23     5     7    14    16
     4     6    13    20    22
    10    12    19    21     3
    11    18    25     2     9

The row products are:

  • 17 * 24 * 1 * 8 * 15=48960
  • 23 * 5 * 7 * 14 * 16=180320
  • 4 * 6 * 13 * 20 * 22=137280
  • 10 * 12 * 19 * 21 * 3=143640
  • 11 * 18 * 25 * 2 * 9=89100

The column products are:

  • 17 * 23 * 4 * 10 * 11=172040
  • 24 * 5 * 6 * 12 * 18=155520
  • 1 * 7 * 13 * 19 * 25=43225
  • 8 * 14 * 20 * 21 * 2=94080
  • 15 * 16 * 22 * 3 * 9=142560

The diagonal products are:

  • 17*5*13*21*9=208845
  • 24*7*20*3*11=110880
  • 1*14*22*10*18=55440
  • 8*16*4*12*25=153600
  • 15*23*6*19*2=78660

The anti-diagonal products are:

  • 15*14*13*12*11=360360
  • 8*7*6*10*9=30240
  • 1*5*4*3*2=120
  • 24*23*22*21*25=6375600
  • 17*16*20*19*18=1860480

The highest value is 6375600, while the lowest is 120. Therefore, the score of this matrix is 6375480. Your Cody score will be the Kurchan score of your matrix.

Solution Stats

96.55% Correct | 3.45% Incorrect
Last Solution submitted on Dec 02, 2019