To approach this problem, we first convert all the times from minutes and seconds into total seconds to make the calculations easier. Then, we'll group them so that the sum of each group is as close to 180 seconds (3 minutes) as possible.

Converting times into seconds:

Time	Total Seconds
0.38	38
2.10	130
1.03	63
1.02	62
0.52	52
1.20	80
0.51	51
0.31	31
0.24	24
0.40	40
0.27	27
2.39	159
0.56	56
0.57	57
0.30	30
0.38	38
0.34	34
0.31	31
0.28	28
1.11	71
0.38	38
0.33	33
0.24	24
0.44	44
1.29	89
0.56	56
0.31	31
0.40	40
0.34	34
0.39	39
0.38	38
1.02	62
0.38	38
0.45	45
2.38	158
0.39	39
1.29	89
0.33	33
1.07	67
0.33	33
0.43	43

Grouping times:

Now we need to group the times so that each group’s total does not exceed 180 seconds (3 minutes) and the totals are as balanced as possible.

I'll calculate this optimally.Here are the groups of times, with each group totaling as close to 180 seconds (3 minutes) as possible, without exceeding it:

1. Group 1: 159 seconds
2. Group 2: 158 seconds
3. Group 3: 130 + 45 = 175 seconds
4. Group 4: 89 + 89 = 178 seconds
5. Group 5: 80 + 71 + 28 = 179 seconds
6. Group 6: 67 + 63 + 44 = 174 seconds
7. Group 7: 62 + 62 + 56 = 180 seconds
8. Group 8: 57 + 56 + 52 = 165 seconds
9. Group 9: 51 + 43 + 40 + 40 = 174 seconds
10. Group 10: 39 + 39 + 38 + 38 + 24 = 178 seconds
11. Group 11: 38 + 38 + 38 + 34 + 31 = 179 seconds
12. Group 12: 34 + 33 + 33 + 33 + 31 = 164 seconds
13. Group 13: 31 + 30 + 27 + 24 = 112 seconds

These groups are well-balanced, with only slight variations in total times.

Would you like a detailed explanation on how to adjust or balance these groups further? Here are five related questions:

1. Would you like to see a breakdown of how I calculated the total seconds for each time?
2. Should I further optimize these groups to minimize the time difference even more?
3. Do you need a different total threshold for each group (other than 180 seconds)?
4. How would you like to handle any specific time constraints or group sizes?
5. Would you like to visualize the differences in group totals?

Tip: When grouping items by constraints, sorting them in descending order helps achieve an optimal arrangement faster.