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The sequences are different in each grid, can you solve all 4 question marks?

Grid 1: enter image description here

Grid 2: enter image description here

Note: Since it are 2 seperate grids, the sequence logic is different.

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I think the answer to the first grid is as follows

enter image description here

Reasoning

Reading the existing grid top-to-bottom and left-to-right gives the sequence $4,8,2,6,2,2,4,8$
We notice that from the 3rd element onwards each number is the product of the previous two modulo $10$,
e.g, $2 \times 6 = 12 \equiv 2\mod 10$
This means that the next element at the top is $4 \times 8 = 32 \equiv \textbf{2}\mod 10$
and the next element at the bottom is $8 \times 2 = 16 \equiv \textbf{6}\mod 10$

Less certain, but I think the answer to the second grid is as follows

enter image description here

Reasoning

This time let us read each column as a single number by concatenating the digits i.e, $89, 18, 16, 12$
In this sequence, each number is just double the second digit (bottom digit) of the previous number,
e.g, $9 \times 2 = 18, 8 \times 2 = 16$
This means the next two-digit number is $2 \times 2 = 4 = 04$.

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