How many squares?

Metal drain cover on a street surrounded by concrete and grass. The drain is made up of small squares, 8 across and 8 down, totalling 64 individual squares.

Prompts

How many squares of all different sizes can be found on this drain cover?

How many rectangles of all different sizes can be found on this drain cover?

In how many different ways could an ant walk along the grate from the top left corner to the bottom right corner? Assume that the ant always walks towards the bottom right corner.

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