Math Puzzle: Find the Unknot

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A chain in each of the following pairs can be untangled in a circle – the so -called unknown. Which one is it?

The graph shows two pairs of mathematical knots labeled

Nodes at the top left and bottom right can be untangled in circles:

Graphic shows how to cancel the first knot of pair 1 in four stages and the second knot of pair 2 in seven stages.

Challenge problem: the other two nodes, which cannot be completely detailed, can each be made to look like one of the four most basic knots. Identify them!

The graph shows four basic nodes: Trefoil, Eight, Cinquefoil and Three-Twist figure.

The upper right node is equivalent to node 2, and the bottom left is equivalent to node 4.

Graphic highlights the second knot of pair 1 along the node with three twists and the first knot of pair 2 alongside the node of figure eight.

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