BS Rule 51: Linking all numbers whose value is a multiple of 2 generates a tight symmetrical gird of diamond-square shapes radiating outward from the Prime Diagonal (PD). 

Note: There are no pure link lines along the PD. Starting with 2, every other 2-based number is excluded from the Strict Inner Grid as: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, ...and is the master exclusion list.

BS Rule 52: Linking all numbers whose value is a multiple of 3 generates a tight symmetrical gird of alternating hexagon-like shapes radiating outward from the Prime Diagonal (PD). 

Note: There are no pure link lines along the PD. Starting with 6, every fourth 3-based number is excluded from the Inner Grid as: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, ...

BS Rule 53: Linking all numbers whose value is a multiple of 4 generates a tight symmetrical gird of diamond-square shapes radiating outward from the Prime Diagonal (PD), overlapping the 2-based numbers, and revealing that all even numbers within the Inner Grid are divisible by 4.

Note: There are no pure link lines along the PD. The same 2-based excluded numbers apply.

BS Rule 54: Linking all numbers whose value is a multiple of 5 generates a symmetrical grid of diamond-squares (3 numbers/side) radiating outward from the PD.

Note: There are no pure link lines along the PD. Starting with 10, every fourth 5-based number is excluded from the Inner Grid: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,...

BS Rule 55: Linking all numbers whose value is a multiple of 6 generates a tight symmetrical gird of diamond-square shapes radiating outward from the Prime Diagonal (PD), overlapping numbers that are both 2- and 3-based.

Note: Simply expands 3 x 2 = 6. There are no pure link lines along the PD. The same 2-based excluded numbers apply.

BS Rule 56: Linking all numbers whose value is a multiple of 7 generates a symmetrical gird of diamond-square shapes radiating outward from the Prime Diagonal (PD).

Note: There are no pure link lines along the PD. Starting with 7, every fourth 7-based number is excluded from the Inner Grid as: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,...

BS Rule 57:  Linking all numbers whose value is a multiple of 8 generates a symmetrical gird of diamond-square shapes radiating outward from the Prime Diagonal (PD) overlapping the 2-based numbers, and revealing that all even numbers within the Inner Grid are divisible by 4.

Note: There are no pure link lines along the PD. The same 2-based excluded numbers apply.

BS Rule 58: Linking all numbers whose value is a multiple of 9 generates a tight symmetrical gird of diamond-square shapes radiating outward from the Prime Diagonal (PD), overlapping numbers that are 3-based.

Note: Simply expands 3 x 3 = 9. There are no pure link lines along the PD. The 9-based excluded Inner Grid numbers, a subset of the 2-based master exclusion list, are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90,....

BS Rule 59: Linking all numbers whose value is a multiple of 10 generates a symmetrical grid of diamond-squares (3 numbers/side) radiating outward from the PD.

Note: There are no pure link lines along the PD. Starting with 10, every other 10-based number is excluded from the Inner Grid: 10, 20, 30, 40, 50, 60,...

BS Rule 60:Linking all numbers whose value is a multiple of 11 generates a symmetrical gird of diamond-square shapes radiating outward from the Prime Diagonal (PD). And the so on for this series.

Note: There are no pure link lines along the PD. Starting with 22, every fourth 11-based number is excluded from the Inner Grid as: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154,...

BS Rule 61: Not strictly a rule of the matrix, just an obvious mathematical manipulation that is useful to remember, take any series of numbers, add them together, the sum, ∑, times 2 will equal the sums of all the pairs of those numbers in that group arranged along a perimeter. The sum, ∑, times 4 will equal the sums of all possible pair combinations of those numbers.

Note:

BS Rule 62: Any equilateral triangle formed in Column C, and labeled A (top), B, © and C, will have the difference, ∆, between the sums, ∑, A+B+© and A+C+© is 8. Simplified: B-C=8

Note: This follows from BS Rule 31, where the ∆ in number values from Column B to C=3, Column C to D=5, Column D to E=7,... and therefore, Column B to D=8 as the columns decrease in value by -1, -3, -5, ...left to right, respectively.

BS Rule 63: The same Rule 62 in reverse, A, ©, B and C (bottom) is true.

BS Rule 64: Following BS Rule 31 ... and similar to Rules 62 and 63 above ... as one moves the triangle to the right, Columns D, E, F,... the difference, ∆, in values goes as: 12, 16, 20, ...

Note: C to E=12, D to F=16, E to G=20, ... and so on.

BS Rule 65: Additions of opposite diagonal number values of any rectangle parallel to the grid axis, are equal.

Note: 

BS Rule 66: The difference, ∆, in the sums, ∑, of the opposite diagonal values of any 2x2 grid point unit diamond-squares = 4, or 2²

Note: 

BS Rule 67: The central number value, ©, of any square or diamond-square equals the sum, ∑, of the perimeter number values divided by the number (quantity, #) of perimeter units, p-units.

Note: ∑_p-units ÷ #_p-units = © 

BS Rule 68: The difference, ∆, in the sums, ∑, of the opposite diagonal number values of any 3x3 grid point unit diamond-squares = 16, or 4².

Note: 

BS Rule 69: The central number value, ©, of any square or diamond-square equals the sum, ∑, of opposite side perimeter number values divided by the number (quantity, #) of perimeter units, p-units.

Note: ∑_p-units ÷ #_p-units = © 

BS Rule 70: The difference, ∆, in the sums, ∑, of the opposite diagonal number values of any 4x4 grid point unit diamond-squares = 36, or 6².

Note: 

BS Rule 71: The central number value, ©, of any square or diamond-square equals the sum, ∑, of opposite side perimeter number values divided by the number (quantity, #) of perimeter units, p-units.

Note: ∑_p-units ÷ #_p-units = ©

BS Rule 72: The central number value, ©, of any square or diamond-square equals the sum, ∑, of symmetrically opposite individual perimeter number values divided by the number (quantity, #) of perimeter units, p-units.

Note: ∑_p-units ÷ #_p-units = ©

BS Rule 73: The difference, ∆, in the sums, ∑, of the opposite diagonal number values of any 5x5 grid point unit diamond-squares = 64, or 8², and so on.

Note: 

BS Rule 74: As in Rules 69, 71, and 72, as the number of perimeter units increase, so do the number of combinations of symmetrically opposite p-unit number values that, when divided by the # of p-units, will = ©.

Note:  

BS Rule 75: Combining the perimeter number values of diamond-squares 2x2, 3x3, 4x4,and 5x5, and dividing by the total number,#, of p-units = ©.

Note: ∑_p-units ÷ #_p-units = ©

BS Rule 76: For a given central number, ©, its horizontal Prime Diagonal, PD_h, number value minus it vertical, PD_v, number value = ©.

Note: PD_h-PDv=© as 100-25=75  Restated: PD_h-Column Value=PD_v

BS Rule 77: For a given central number, ©, the difference,∆, between it and the 1^st vertical number value above it is found on the 1^st Diagonal intersecting that row. 

For a given central number, ©, the difference,∆, between it and the 2^nd vertical number value above it is found on the 2^nd Diagonal intersecting that rowr.

For a given central number, ©, the difference,∆, between it and the 3^rd vertical number value above it is found on the 3^rd Diagonal intersecting that row, and so on.

Note: Restated: The ∆ between © and the column # value above, can be found on the row of its PD_h.

BS Rule 78: Similarly, for a given central number, ©, the difference, ∆, between it and the 1^st horizontal row number towards the PD is found vertically in the column above © on the 1^st Diagonal intersecting that column.

For a given central number, ©, the difference, ∆, between it and the 2^nd horizontal row number towards the PD is found vertically in the column above © on the 2^nd Diagonal intersecting that column.

For a given central number, ©, the difference, ∆, between it and the 3^rd horizontal row number towards the PD is found vertically in the column above © on the 3^rd Diagonal intersecting that column, and so on.

Note: Restated: The ∆ between © and the row # towards the PD, can be found on the column of its PD_v. 

BS Rule 79: Similarly, for a given central number, ©, the difference, ∆, between it and the 1^st horizontal row number away from the PD is found vertically in the column above that 1^st horizontal row # on the 1^st Diagonal intersecting that column.

For a given central number, ©, the difference, ∆, between it and the 2^nd horizontal row number away from the PD is found vertically in the column above that 2^nd horizontal row # on the 2^nd Diagonal intersecting that column.

For a given central number, ©, the difference, ∆, between it and the 3^rd horizontal row number away from the PD is found vertically in the column above that 3^rd horizontal row # on the 3^rd Diagonal intersecting that column, and so on.

Note: Restated: The ∆ between © and the row # away from the PD, can be found on the row of its respective vertical PD_v.

BS Rule 80: Similarly, for a given central number, ©, the difference, ∆, between it and the 1^st vertical column number below, away from the PD is found horizontally in the row where the the 1^st Diagonal intersects.

For a given central number, ©, the difference, ∆, between it and the 2^nd vertical column number below, away from the PD is found horizontally in the row where the the 2^nd Diagonal intersects.

For a given central number, ©, the difference, ∆, between it and the 3^rd vertical column number below, away from the PD is found horizontally in the row where the the 3^rd Diagonal intersects.

Note: Restated: The ∆ between © and the column of #s below, away from the PD, can be found on the column below ©’s respective horizontal PD_h.