|
2020-02-27, 21:44
|
#1 |
|
Dec 2019
Kansas
24 Posts |
March 2020
|
|
|
|
2020-04-24, 05:46
|
#2 |
|
Jan 2020
22×7 Posts |
What about tiling an infinite board?
Asymptotically, leave a fraction r of empty squares, and place each symbol in 1/3 of the remaining squares; ensure winning chance for no player.
Can you do so for some explicit fraction r>0? Can you state (and eventually reach) some upper bound on r? Let's make "asymptotically" more precise. Weak version: choose some square as the origin, consider a (2L-1)x(2L-1) board centered around it and find the fraction r(L) of empty squares; take the limit as L grows to infinity. Strong version: for each square, consider the four 1xL boards with a corner on it (along the directions +x,-x,+y,-y); as L grows to infinity, the four limits must be equal, and such value must not change for different choices of the starting square. Last fiddled with by 0scar on 2020-04-24 at 05:56 |
|
|
|
 |
| Thread Tools | |
Similar Threads
|
||||
| Thread | Thread Starter | Forum | Replies | Last Post |
| March 2019 | Xyzzy | Puzzles | 6 | 2019-04-04 16:32 |
| March 2018 | Xyzzy | Puzzles | 2 | 2018-04-08 13:45 |
| March 2017 | R. Gerbicz | Puzzles | 1 | 2017-04-03 10:57 |
| March 2016 | Xyzzy | Puzzles | 21 | 2016-06-09 20:26 |
| gmp 4.2 due in March | Mystwalker | GMP-ECM | 4 | 2006-02-01 12:00 |
