Quantitative Assignment

    $$
    \text{Right} = \text{Bottom}^2
    $$
    $$
    16 = 4^2
    $$
    $$
    16 = 16
    $$

    $$
    \text{Left} = (\text{Top} \times \text{Bottom}) + (\text{Bottom} \times (\text{Top} + 1))
    $$
    $$
    52 = (6 \times 4) + (4 \times (6 + 1))
    $$
    $$
    52 = 24 + (4 \times 7)
    $$
    $$
    52 = 24 + 28
    $$
    $$
    52 = 52
    $$
*   All numbers are consistent with the identified patterns.

    $$
    \text{Left} = \text{Top}^2
    $$
    $$
    49 = 7^2
    $$
    $$
    49 = 49
    $$

    $$
    \text{Right} = \text{Bottom}^2
    $$
    $$
    \text{Right} = 8^2
    $$
    $$
    \text{Right} = 64
    $$
*   The missing number is $\boxed{\text{64}}$.

    $$
    \text{Left} = \text{Top}^2
    $$
    $$
    100 = 10^2
    $$
    $$
    100 = 100
    $$

    $$
    \text{Right} = (\text{Top} \times \text{Bottom}) + \text{Top}^2 + 1
    $$
    $$
    \text{Right} = (10 \times 12) + 10^2 + 1
    $$
    $$
    \text{Right} = 120 + 100 + 1
    $$
    $$
    \text{Right} = 221
    $$
*   The missing number is $\boxed{\text{221}}$.

    $$
    \text{Right} = (\text{Bottom} \times \text{Top}) - (\text{Bottom} \times 8)
    $$
    $$
    255 = (15 \times 25) - (15 \times 8)
    $$
    $$
    255 = 375 - 120
    $$
    $$
    255 = 255
    $$

    $$
    \text{Left} = (\text{Top} \times \text{Bottom}) - (\text{Top} \times 5)
    $$
    $$
    \text{Left} = (25 \times 15) - (25 \times 5)
    $$
    $$
    \text{Left} = 375 - 125
    $$
    $$
    \text{Left} = 250
    $$
*   The missing number is $\boxed{\text{250}}$.

    $$
    \text{Middle} = (\text{Top} + \text{Bottom}) \times 2
    $$
    $$
    12 = (3 + 3) \times 2
    $$
    $$
    12 = 6 \times 2
    $$
    $$
    12 = 12
    $$

    $$
    \text{Right} = \text{Middle} \times 3
    $$
    $$
    36 = 12 \times 3
    $$
    $$
    36 = 36
    $$

    $$
    \text{Left} = \text{Top}
    $$
    $$
    \text{Left} = 3
    $$
*   The missing number is $\boxed{\text{3}}$.

    $$
    \text{Left} = \text{Top} + \text{Bottom}
    $$
    $$
    9 = 2 + 7
    $$
    $$
    9 = 9
    $$

    $$
    \text{Middle} = (\text{Top} \times \text{Bottom}) \times \text{Left}
    $$
    $$
    126 = (2 \times 7) \times 9
    $$
    $$
    126 = 14 \times 9
    $$
    $$
    126 = 126
    $$

    $$
    \text{Right} = \text{Middle} \times 3
    $$
    $$
    \text{Right} = 126 \times 3
    $$
    $$
    \text{Right} = 378
    $$
*   The missing number is $\boxed{\text{378}}$.

    $$
    \text{Middle} = (\text{Top} \times \text{Bottom}) \times 8
    $$
    $$
    16 = (1 \times 2) \times 8
    $$
    $$
    16 = 2 \times 8
    $$
    $$
    16 = 16
    $$

    $$
    \text{Right} = \text{Middle} \times 2
    $$
    $$
    32 = 16 \times 2
    $$
    $$
    32 = 32
    $$

    $$
    \text{Left} = \text{Top}
    $$
    $$
    \text{Left} = 1
    $$
*   The missing number is $\boxed{\text{1}}$.

    $$
    \text{Middle} = \text{Top} \times \text{Bottom}
    $$
    $$
    16 = 4 \times 4
    $$
    $$
    16 = 16
    $$

    $$
    \text{Right} = \text{Middle} \times 4
    $$
    $$
    64 = 16 \times 4
    $$
    $$
    64 = 64
    $$

    $$
    \text{Left} = \text{Top}
    $$
    $$ \