Problem: Text: Since each location on the board can be either empty, black, or white, there are a total of 3 possible board positions on a square board with length n; however only part of them are legal. Tromp and Farneback derived a recursive formula for legal positions L ( m , n ) (\displaystyle L(m,n)) of a rectangle board with length m and n. The exact number of L ( 19 , 19 ) (\displaystyle L(19,19)) is obtained in 2016. They also find an asymptotic formula L A B m + n C m n (\displaystyle Lpprox AB^(m+n)C^(mn)) , where A 0.8506399258457145 (\displaystyle Approx 0.8506399258457145) , B 0.96553505933837387 (\displaystyle Bpprox 0.96553505933837387) and C 2.975734192043357249381 (\displaystyle Cpprox 2.975734192043357249381) . It has been estimated that the observable universe contains around 10 atoms, far fewer than the number of possible legal positions of regular board size (m=n=19). As the board gets larger, the percentage of the positions that are legal decreases.

Question: are there more moves in go than atoms in the universe?
A: yes

Problem: Text: In the first two seasons of the Great Food Truck Race, the competitors were seasoned, professional food truck operators who were competing for a cash prize (first season was $50,000 and second season was $100,000). In the following seasons (save for season six), food trucks were provided to novices (from home cooks to former restaurateurs) who have dreamt of owning and operating their very own food truck. In seasons three, four, and five, the winning team got the money and got to keep the food truck they were provided by the show. In season six and onward, the show reverted to awarding the winning teams only the $50,000.

Question: great food truck race do they get to keep the car?
A: no

Problem: Text: Euryhaline organisms are able to adapt to a wide range of salinities. An example of a euryhaline fish is the molly (Poecilia sphenops) which can live in fresh water, brackish water, or salt water. The green crab (Carcinus maenas) is an example of a euryhaline invertebrate that can live in salt and brackish water. Euryhaline organisms are commonly found in habitats such as estuaries and tide pools where the salinity changes regularly. However, some organisms are euryhaline because their life cycle involves migration between freshwater and marine environments, as is the case with salmon and eels.

Question: can some fish live in both saltwater and freshwater?
A:
yes