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Now lift the rope 1 metre above the ground everywhere. How much extra rope would you need to go around the earth

Now allow circle A to roll around the perimeter of circle B and return to where it started. How many times will circle A have rotated?

This one is super easy because it's been in the news.

Most of the pices look like you only need to follow a diagonal through the big square and mark some half-way points along the square (and you could do that). However, for the small square, I'm not sure how high up the big square it is supposed to go. If I'm right, the diagonal of the small square piece is 1/2 the length of the side of the big square.

Mark the small circle at the contact point with the large circle and rotate until that point again touches the large circle: at 90degrees it will contact the large circle again and again at 180, 270 and 360degrees

a brief reading leads to a misplaced confidence that I have it "cracked".