MathDB

Santa Claus plays a guessing game with Marvin before giving him his present. He hides the present behind one of

100

doors, numbered from

1

100

. Marvin can point at a door, and then Santa Claus will reply with one of the following words:

\bullet

"hot" if the present lies behind the guessed door,

\bullet

"warm" if the guess is not exact but the number of the guessed door differs from that of the present’s door by at most

5

\bullet

"cold" if the numbers of the two doors differ by more than

5

.
At least how many such guesses does Marvin need, so that he can be certain about where his present is?
Marvin does not necessarily need to make a "hot" guess, just to know the correct door with

100\%

certainty.

Problem Statement