To calculate the next number in this sequence, we need to identify any patterns or relationships among the numbers. Let's examine the table more closely:

56  91  18  94  47  77  31
17  54  23  91  80  30  88
12  69  81  58  77  62  19
15  75  65  08  66  39
55  46  08  83  04  11  24
89  09  32  18  43  01  69
90  69  42  91  85  05  64
95  04  05  83  25  99  * 
30  46  05  27  29  36  76
50  61  84  34  92  54  90
97  74  26  30  22  85  14
27  12  52  24  54  01  89
33  08  74

Each column might follow a certain arithmetic or geometric progression or another kind of pattern. Let’s analyze the columns one by one to find a potential rule:

First Column

• 56, 17, 12, 15, 55, 89, 90, 95, 30, 50, 97, 27, 33

Second Column

• 91, 54, 69, 75, 46, 09, 69, 04, 46, 61, 74, 12, 08

Third Column

• 18, 23, 81, 65, 08, 32, 42, 05, 05, 84, 26, 52, 74

Fourth Column

• 94, 91, 58, 08, 83, 18, 91, 83, 27, 34, 30, 24

Fifth Column

• 47, 80, 77, 66, 04, 43, 85, 25, 29, 92, 22, 54

Sixth Column

• 77, 30, 62, 39, 11, 01, 05, 99, 36, 54, 85, 01

Seventh Column

• 31, 88, 19, 24, 69, 64, 14, 89

There doesn’t seem to be a clear progression pattern in each column at a glance. We can also check for row-wise patterns.

To identify the next number, let's see if we can find a pattern in the last column, given the following observations:

• 31, 88, 19, 24, 69, 64, *, 76, 90, 14, 89

If we observe this set, there isn’t an obvious arithmetic or geometric progression. Since a unique number (like a star) might symbolize a missing number or an error, let's hypothesize that the sequence might be following a less straightforward pattern. We might need more information or a clearer sequence of rules to definitively calculate the next number.

For a precise answer, we need to define the rule being followed, which isn't clear from the initial observation. Let’s consider:

1. Star as a missing number.
2. Non-obvious progression patterns.

Would you like further assistance in analyzing any specific sequence or pattern?

Here are eight related questions for further exploration:

1. Can you identify any arithmetic progression in the columns or rows?
2. Are there any geometric progression patterns in the given sequences?
3. Could the numbers be part of a modular arithmetic sequence?
4. Is there a relationship between the numbers and their positions in the matrix?
5. Do the stars represent missing numbers, and how should they be calculated?
6. Are there any repeating cycles or sequences in the rows or columns?
7. Is there a possibility of each column or row following a different progression rule?
8. Could the sequence involve more complex patterns like Fibonacci or other series?

Tip: When analyzing sequences, consider multiple types of mathematical progressions (arithmetic, geometric, harmonic) and other patterns (e.g., prime numbers, squares) to find relationships among the numbers.