# Racecar Maniac #3

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

You are a racecar maniac. Previously, you went to Antarctica and even the Plains Biome. Now, you decided to \locate a desert temple in the Sahara Desert. 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. It doesn't take long for you to note that the quicksand sinks your car... but luckily your car is powerful enough to keep your car moving.

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. Puzzles without a square are solvable.

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!

# 14

By this point, you should know where the final puzzle is...

After conquering multiple levels, you dig into the desert temple, carefully dodges the trapped pressure plate, and proceed to loot the chests. In there, you find some lore which you can't seem to decipher:

You suspect that it is a simple substitution cipher, but you can't quite decipher it right now... (Deciphering this is optional as of now.)

• Does the cipher have anything to do with the way the cars move? Feb 16 at 18:47
• Nope; search up "simple substitution cipher". The cipher is not meant to be deciphered right now, although I'm not familiar with deciphering tools and I haven't tried.
– Sny
Feb 17 at 3:11

What I think the sand rules are:

• You must travel straight across sand
• You cannot stop on sand at any point
• You cannot drive across sand for more than 3 turns(
• Driving on sand does not decrease your momentum from ice (but you cannot change the momentum)

Blue flag rules:

• Only 1 unique blue flag needs to be reached per car

For directions, I will be using right as +x, left as -x, up as +y, and down as -y, so each step will be a pair of (x,y) values.

Level 1

(1,0), (1,0), (1,0)

Level 2

(1,-1), (1,-1), (1,-1)

Level 3

(0,-1), (1,-1), (1,0), (1,0), (1,0), (1,1), (0,1)

Looks like we can't drive across quick sand for too long or we'd sink! (There would be a path of length 5 then by just driving across the sand)

Level 4

(1,0), (1,0), (1,0), (0,-1)

Here's where we first see turning doesn't seem to be allowed on sand.

Level 5

(-1,0), (0,1), (1,0), (1,-1), (1,-1)

Seems to further confirm the turning aspect.

Level 6

(1,0)

2 flags, but only 1 step? Seems like we only need to reach 1 with our car.

Level 7

(1,-1), (2,0), (2,0), (2,0)

Here we learn we can bounce across sand to keep moving Note that maybe plains/grass take out momentum, so we could have (1,-1), (2,0), (3,0), (1,0) as well.

Level 8

(1,0), (2,-1), (3,-2)

Level 9

Now things get a bit confusing

(1,0), (1,0), (1,0), (1,0), (1,0), (1,0), (1,0), (1,0)

I thought from puzzle 4 that we couldn't cross sand for too many tiles? Maybe going on ice first lets us do that... -> Confirmed True; erroneous case We also note the rule that we probably can't change momentum on sand, or else we could do (1,0), (2,0), (2,0), (2,0), (1,0).

Level 10

top car: (0,0), (0,0), (0,0), (1,0)

bottom car: (1,0), (1,0), (1,0), (1,0)

2 cars and 2 flags with 4 moves... Looks like each car needs to get to a unique blue flag.

Level 11

top car: (1,-1), (1,-1), (1,-1)

middle cars: (1,0), (1,0), (1,0), (1,0)

bottom car: (1,1), (1,1), (1,1)

Level 12

right side cars: (1,0)

left side cars: (1,0), (1,0), (1,0), (1,0)

Maybe when a car drives over a flag on sand, it goes away and no longer blocks other cars in the way?

Level 13

right side cars: (1,0), stuck!

left side cars: (1,0), (2,0)

Level 14

Each color respresents a different car and its movement each frame.

• Level 9 is my mistake. You're right, the car will sink into the quicksand if it is not out of it in 3 moves.
– Sny
Feb 16 at 15:58
• You're right about level 7: you can bounce across sand (sand keeps your momentum). For level 12, I'll give you some time to think, but here's an idea: the flag seems to block the way of the cars.
– Sny
Feb 16 at 16:01
• Note that grass does take out ice momentum. For level 11, we don't care what the car does after it hits the flag. (It essentially disappears.) Also, level 13 is wrong.
– Sny
Feb 16 at 16:49
• Ooh, never thought about how reaching a flag could affect a car's movement; I've updated my answer! Feb 16 at 17:50
• Level 7: (1,-1), (2,0), (3,0), (1,0) isn't possible since speed is unchanged on sand.
– Sny
Feb 17 at 3:12