OFFSET
1,2
COMMENTS
The problem is the following.
You are given an empty n X n grid. You can place some reflectors into the cells of the grid.
This arrangement consists of thin flat plates, each of which is rotatably mounted about a vertical axis so that two angular positions relative to the grid axes, namely plus and minus 45 degrees, are possible. A particle is shot into this arrangement and when it hits a reflector, it is deflected by 90 degrees without any loss of momentum according to the reflector's current orientation. After a reflector has been hit by the particle, it rotates by 90 degrees and maintains this position until the next hit. Not every grid position has to be assigned a reflector -- grid positions without reflectors are permitted.
LINKS
Benjamin Butin, a(3) = 18
Benjamin Butin, Exponential lower bound for A350155
Dmitry Kamenetsky, Laser and mirrors on a 4x4 grid, Puzzling StackExchange, November 2021.
Dmitry Kamenetsky and Daniel Mathias, Optimal solutions for n <= 6
Dmitry Kamenetsky and Benjamin Butin, Improved patterns.
Topcoder, Marathon Match 132: BouncingBalls.
FORMULA
a(n) >= 3*2^n-6, this value can be obtained with a simple pattern (see links above). - Benjamin Butin, Jan 20 2022
EXAMPLE
See links for examples.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Dmitry Kamenetsky, Dec 17 2021
EXTENSIONS
a(3) corrected and a(4)-a(6) confirmed by Benjamin Butin, Jan 20 2022
STATUS
approved