Mintonette has a long yet forgotten history. This ruleset appeared as a Nikoli Omopa type in the mid-90s (with slightly less flexibility in its presentation), but it didn't seem to catch on. It later appeared on Puzzle Picnic, but in a much stricter form where all the clue values are equal. (Which is pretty silly, in my opinion; part of the appeal with this genre lies in the interactions between small and large clue values.) Its current form was popularized by Toketa vol. 11, and it has seen a small yet significant resurgence since then.
This genre has a lot of potential! There have been other genres which count numbers of turns (e.g. Detour), but allowing these counts to play out through different strands creates some cool interactions.
Rules: Draw paths through the centers of cells connecting each circle to exactly one other. Paths may not cross each other or themselves, and every cell must be used by a path. If a circle contains a number, it indicates the number of turns taken by the path containing that circle.
Both of today's puzzles are tricky. The first puzzle starts off easy but ramps up in difficulty fairly quickly (though still solves cleanly with the right deductions). The second grid builds off the first and introduces a few other ideas common in the genre. The following fact may prove helpful when solving both puzzles (encoded via rot13): Gur cnevgl bs n pyhr pryy pna gryy lbh ubj gur pbeerfcbaqvat cngu ragref naq rkvgf vgf raqcbvagf. Sbe rknzcyr, vs n cngu rkvgf na bqq pyhr iregvpnyyl, vg zhfg ragre vgf bgure pvepyr ubevmbagnyyl.
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