Avoid the Car Crash
(Published on 25. July 2025, 14:00 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply.
Each grey car moves in arrow direction with an initial velocity “v” in units of cells per second as given by the digit it contains.
The car drivers are not paying close attention and suddenly notice the red stop sign one cell in front of them. They immediately hit the brakes and decelerate with constant deceleration “a” in units of cells per second squared as given by the digit in the stop sign. Some manage to stop in the cell of the stop sign but some overshoot. According to the laws of physics, the travel distance “x” is given by the initial velocity squared and divided by twice the deceleration, i.e., x = v2/(2a). All travel distances must be integer numbers of cells.
The track of a car is the collection of all cells that it visits, including its initial and final cells. For example, if x = 2, the track occupies 3 cells. Tracks must not have any mutual overlap and they must not extend beyond the Sudoku grid.
The digit 5 acts as an obstacle and must not appear on any track.
Your feedback, ratings and comments are highly appreciated. Have fun!
Background: The relationship between braking distance and constant deceleration is actually as stated in the puzzle. Formally, this is a uniformly accelerated movement, whereby the acceleration acts in the opposite direction to the initial velocity and therefore reduces it.
For a version with related physics where you have to avoid crashes between spaceships instead of between cars, you may want to consider this puzzle on the Special Theory of Relativity, though the solving mechanic there is quite different.
Solution code: All digits of row 4 (from left to right) followed by column 6 (from top to bottom) without spaces.
Comments
yesterday, 12:32 by bhambells
A daunting rule set, but actually resolves quite smoothly when you pick your way through it. One of those rare occasions when I seemed to look in the right place every time.
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Glad you enjoyed it! Thanks for commenting. - TB
on 28. July 2025, 22:04 by NotSoMagnifique
Hard but worth it once I started figuring out the implications of the equations! (Slight bifurcation at the end though)
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I am happy that you liked it, thanks for commenting! Bifurcation should not be necessary, but gladly you managed to finish it anyway. - TB
on 25. July 2025, 17:47 by Marshal on Mars
Is a car's starting cell included in its travel distance, or does its travel distance start with the Stop sign? Or is it ambiguous and to be deduced?
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The travel starts in the initial cell of the car, not in the cell of the stop sign. I tried to express this in the rules with the statement that the track contains the initial and final cells. The example for x = 2 means that the car starts in the initial cell that contains the sketch of a car. If it then moves by two cells, i.e., takes two steps from where it starts, it will have passed one cell beyond the stop sign, occupying a total of three cells. - TB
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Thanks for clarifying! I was thrown off by "travel distance" and "track" being two separate terms. - M
on 25. July 2025, 16:11 by halvorlinder
Nice puzzle!
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Thank you! - TB
on 25. July 2025, 15:28 by sanabas
Had fun testing this.
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Glad you liked it, and many thanks for your suggestions during the testing phase! - TB
