Integer Solution:

triple [1,2,5] - Cost: 3
triple [2,19,16] - Cost: 4
triple [3,13,3] - Cost: 3
triple [4,12,28] - Cost: 4
triple [5,14,23] - Cost: 4
triple [6,29,24] - Cost: 4
triple [7,27,22] - Cost: 4
triple [8,32,19] - Cost: 4
triple [9,8,12] - Cost: 4
triple [10,3,15] - Cost: 4
triple [11,28,17] - Cost: 5
triple [12,22,8] - Cost: 4
triple [13,23,33] - Cost: 4
triple [14,11,1] - Cost: 4
triple [15,16,2] - Cost: 4
triple [16,20,7] - Cost: 4
triple [17,9,18] - Cost: 4
triple [18,7,13] - Cost: 5
triple [19,18,9] - Cost: 4
triple [20,25,25] - Cost: 3
triple [21,10,10] - Cost: 4
triple [22,33,11] - Cost: 4
triple [23,1,14] - Cost: 3
triple [24,17,31] - Cost: 4
triple [25,31,27] - Cost: 4
triple [26,5,20] - Cost: 4
triple [27,26,29] - Cost: 4
triple [28,4,30] - Cost: 4
triple [29,6,32] - Cost: 4
triple [30,15,4] - Cost: 4
triple [31,24,26] - Cost: 5
triple [32,21,21] - Cost: 4
triple [33,30,6] - Cost: 4
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Total Costs: 131