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Attribution: Inspired by Racetrack in Ben Orlin's Math Games with Bad Drawings

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You are a racecar maniac. Previously, you have decided that Antarctica is the nicest place to race your car, so of course you go to Antarctica. However, now you decide to venture into the plains biome. (You seem to have forgotten where; you just decided to \locate and \tp ...) Your goal is to lead the car to the flags. The rules are intentionally not precise, since you will have to figure out how the car works yourself. However, you quickly realize that due to the friction of the new grass, you can't maintain high velocities... and also the car stops turning after a certain threshold.

The squares on the top right (if present) indicates the length of the common path: a number in green is the time required (in frames) to reach the flag. A red box indicates that the puzzle is not possible to be solved. The optimal path is not necessarily unique.

A complete answer should solve all 14 puzzles. For solvable puzzles, give the solution. Otherwise, demonstrate that the puzzle is not solvable. Partial answers are allowed and encouraged.

Have fun racing!

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It must be somewhere...

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1 Answer 1

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Full solution

1, 2, 3

Rule 1: The speed of the car is 1 square/frame on grass.

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Rule 2: Every flag must be reached by the car.

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Rule 3: The car is able to turn 45 degrees or 90 degrees sideways.

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Rule 4: The car cannot turn at an angle that is greater than 90 degrees.
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8, 9

Rule 5: The car can go back to already visited squares.

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Rule 6: Multiple cars travel at the same time.

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Rule 7: Multiple cars cannot be on the same square at the same time, but can on different frames. (collision)

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There are 43 flags for 3 cars, so the optimal solution must have at least 15 frames. A solution in 15 frames is possible:

enter image description here

Note the two cars on the top don't cross their intersection on the same frame, such that no collision happens.

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Level 14 is once again hidden in the title. As pointed out by @ibanezplyr in the comments, this one needs to be solved using both physics from this puzzle and the previous one! Here's a solution in 84 frames.
enter image description here

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    $\begingroup$ Good answer! V oryvrir gur syntf va V A naq F ner ernpunoyr vs lbh hfr gur vpr culfvpf sebz gur svefg chmmyr. Guvax gbc ubyr va gur N gb fvqr bs gur V. $\endgroup$
    – ibanezplyr
    Commented Feb 15 at 21:08
  • $\begingroup$ Oh you’re totally right! I’ll edit my answer $\endgroup$
    – Jujustum
    Commented Feb 15 at 21:19
  • $\begingroup$ Gur pne vf nyybjrq gb erirefr ba vpr. Lbh pna fnir n zbir jura lbh rkvg gur N gb znxr gur whzc gb gur V ol tbvat fgenvtug, naq gura gheavat nebhaq engure guna rkvgvat ng n sbhegl-svir qrterr natyr. Jvgu gung fnvq, V pbhag rvtugl-rvtug zbirf va lbhe pheerag fbyhgvba. Gur erirefr gevpx fubhyq oevat vg onpx qbja gb rvtugl-frira. Hayrff V zvffrq nabgure whzc fbzrjurer, V qvq pngpu gur whzc sebz gur Y gb gur N, naq pbhagrq gubfr gjb fcnprf nf bar zbir. $\endgroup$
    – ibanezplyr
    Commented Feb 15 at 21:42
  • $\begingroup$ Hmm, I don't think you can make some of the moves on ice... did you check the accepted solution? $\endgroup$
    – Sny
    Commented Feb 16 at 2:13
  • $\begingroup$ ^ did you check the accepted solution for puzzle #1? $\endgroup$
    – Sny
    Commented Feb 16 at 4:43

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