Saturday, 2 September 2017

Three Puzzles

Here are 3 puzzles to put your mind to, with 2 of them being related to chess, to some degree.

  1. How many distinct ways can 6 knights be placed on a 4 by 4 chess board, so that no knight attacks another knight? (And by distinct, rotations don't count as a separate solution)
  2. How many ways can N Queens be placed on a NxN chess board so that no queen attacks another queen? (NB There has been a flurry of reporting suggesting a solution to this problem will win you $1,000,000. In fact the prize is for solving the P v NP problem, of which this is just one example of an NP problem)
  3. N students are playing a variant of 'Duck, Duck, Goose'. In this variant, Student 1 goes around the ring of players (which now excludes Student 1), announcing Duck N-1 times, and Goose the Nth time. Student 1 then sits out while the 'Goose' repeats the process. Who is the last student to be the Goose?

1 comment:

adamponting said...

Q1. uh... 47?
(my Cython program plus primitive printout of the positions here )