MathDB

A tourist has arrived on an island where

100

wizards live, each of whom can be a knight or a liar. He knows that at the time of his arrival, one of the hundred wizards is a knight (but does not know who exactly), and the rest are liars. A tourist can choose any two wizards

A

and

B

and ask

A

to spell on

B

with the spell "Whoosh"!, which changes the essence (turns a knight into a liar, and a liar into a knight). Wizards fulfill the tourist's requests, but if at that moment wizard

A

is a knight, then the essence of

B

really changes, and if

A

is a liar, that doesn't change. The tourist wants to know the essence of at least

k

wizards at the same time after several consecutive requests. For which maximum

k

will he be able to achieve his goal?

Problem Statement