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A "brute-force" approach to this problem is doubtful :

Such an approach would generate all possible sim of 16 terms, each representing one quadruplet $i, j, k, l \in \{0, \dots, 5\}$. Since there are $6^4=1296$ such potential summation terms, there are ${6^4}^{16}$ possible 16-terms sums.But :

sage: (6^4)^16.log(10).n()
5596.93006676446

meaning that the number of sums is about $8.51\cdot 10^{5596}$, which seems a bit too large for systematic exploration...

Limiting the size of the exploration by other means is necessary. But this is the feathers of a totally different horse...

HTH, but doubting it,

A "brute-force" approach to this problem is doubtful :

Such an approach would generate all possible sim sum of 16 terms, each representing one quadruplet $i, j, k, l \in \{0, \dots, 5\}$. Since there are $6^4=1296$ such potential summation terms, there are ${6^4}^{16}$ possible 16-terms sums.But :

sage: (6^4)^16.log(10).n()
5596.93006676446

meaning that the number of sums is about $8.51\cdot 10^{5596}$, $6.44\cdot 10^{49}$, which seems a bit too large for systematic exploration...

Limiting the size of the exploration by other means is necessary. But this is the feathers of a totally different horse...

HTH, but doubting it,

A "brute-force" approach to this problem is doubtful :

Such an approach would generate all possible sum of 16 terms, each representing one quadruplet $i, j, k, l \in \{0, \dots, 5\}$. Since there are $6^4=1296$ such potential summation terms, there are ${6^4}^{16}$ possible 16-terms sums.But :

sage: ((6^4)^16).log(10).n()
49.8016800245532
49.8016800245532