A301426 Number of steps required in the worst case for three knights to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).

1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7, 8, 8

Offset: 1

Author

Dmitry Kamenetsky, Mar 21 2018

Keywords

• nonn
• more

Comments

The main entry for this problem is A300576. In this version there are three knights who are searching for the princess; each knight can search a different room.

Links

• Dmitry Kamenetsky, Optimal solutions

Crossrefs

Cf. A300576, A301337.

Formula

It seems that for n >= 3:

if n = 3 mod 5, then a(n) = (n - 3)/5*2 + 1,

otherwise a(n) = floor((n - 4)/5)*2 + 2.

This conjecture is a(n) = A194222(n) for n>2. - R. J. Mathar, Mar 27 2025