List 1: Write down the numbers 1 to 99

1, 2, 3, 4, 5, 6, 7, 8, 9, ..., 99

List 2: Take every successive set of three numbers (3k-2, 3k-1, 3k) for k=(1...33) and randomly apply a permutation to the trio. Example:

3, 1, 2, 4, 5, 6, 7, 9, 8, ..., 98

List 3: Multiply the first numbers, second numbers, etc of lists 1 and 2. Example:

3, 2, 6, 16, 25, 36, 49, 72, 72, ..., 9702

What is the expected sum of the values in list 3?

When I found and solved the problem this is based on, I found it had a lot of nice underlying mathematical structure.  I challenge you then, to find a solution analytically.

Posted by Jer on 2024-09-28 18:47:33