Stretch goal: optimize problems to run in less than 1 second.

More realistic goal: optimize problems to run in less than 1 minute.

Problem  1:     6118 μs (866436, 276650720)
Problem  2:     6497 μs (542, 360)
Problem  3:     7776 μs (232, 3952291680)
Problem  4:     9161 μs (219, 127)
Problem  5:     4277 μs (991, 534)
Problem  6:     6594 μs (6726, 3316)
Problem  7:    21934 μs (205, 80902)
Problem  8:     9248 μs (1217, 501)
Problem  9:     2463 μs (22477624, 2980044)
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Total:         74068 μs