Black eyes and blue eyes

To win the hand of his ladylove, Beremiz had to solve one last challenge
in front of the Caliph. Five slave girls, each one covered with a veil,
were presented to Beremiz. He was told that two of them had black eyes
and always told the truth, while the other three slaves had with blue
eyes and always lied. Beremiz should deduce the color of the eyes of all
the slaves with only three questions.

Beremiz began by asking the first slave:

“What color are your eyes?”

Surprisingly, the answer was given in a dialect that was only
understandable to the slaves. Considering the protest of Beremiz, the
Caliph ordered that the rest of answers were given in Arabic. Despite
the setback, Beremiz went on, and asked the second slave:

“¿What was the reply that your companion just gave?”

“She said: My eyes are blue.”

Finally, Beremiz asked the third slave:

“What color are the eyes of those two slaves that I have just
questioned?”

“The first girl has black eyes and the second has blue eyes.”

After that answer, Beremiz deduced with certainty the color of the eyes
of the five slaves (the first had black eyes, the second blue, the third
black, and the last two blue), and so he won the hand of his beloved
Telassim.

Input

Input consists of several cases, each with two natural numbers x and y
between 0 and 10⁴.

Output

Every case corresponds to a variant of the problem, where there are x
slaves with black eyes and y slaves with blue eyes. You can only ask
“Which is the color of the eyes of slave number i?” to the first slave,
for all i between 1 and x + y.

Print the minimum number of questions needed to deduce the color of the
eyes of each slave by using an optimal strategy, assuming the best and
the worst luck in the answers. If it is impossible to tell no matter how
many questions are asked, print “no”.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T10:36:33.847Z

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