A chandlery of tangles.
What a knot really is, one tuck at a time.
Every tangle in the chandlery is a loop of rope with crossings — some pass over, some pass under. You may only touch it three ways: tuck a curl through itself, poke a canceling pair apart, or slide two overlapping passes past each other.
UNTIE IT: find the moves that bring a tangle back to a clean loop. TIE THE BEND: reach a target shape in as few moves as you can. SAME OR DIFFERENT: two tangles, one question — are they secretly the same knot?
Tap a crossing to see what's legal there. There's no penalty for looking — only for guessing wrong on SAME/DIFFERENT, where your streak is at stake.
Some tangles cannot be untied, ever, by any sequence of these moves. Proving you believe that — correctly — is its own kind of puzzle.