Question

this particular sequence, the knight made 8 moves. Can we always
y that the number of moves made by knight must be even?
f your answer is yes, prove it! Else, demonstrate a sequence of moves
n which the knight returns to al but makes an odd number of moves.
www.learnsmart.in​

Answer 1

Given:

The knight made 8 moves.

To find:

Can we always  say that the number of moves made by knight must be even?

Solution:

Schwenk proved that for any a × b board with a ≤ b, a closed knight's tour is always possible unless one or more of these three conditions are met, those are,  

a = 1, 2, or 4

a and b are both odd

a = 3 and b = 4, 6, or 8.