# Guess game of Dwarfs [closed]

Kate and N dwarfs are playing a dwarf guessing game. In the beginning there are five empty boxes numbered with the numbers 1, 2, 3, 4 and 5. According to the rules of the game, Kate places at least 1 and at most 9 marbles in each box such that the number of marbles in box n for each n <m is not more than the number of marbles in box m. Not knowing how many marbles are in which box, each of the N dwarfs makes a separate guess for each box with numbers 1, 2, 3, 4, and 5. Accordingly, N dwarf estimates 5N in total. No matter how Kate puts the balls, what would N be at least if N dwarves agree to ensure that at least one of these 5N guesses is correct?

• Welcome to Puzzling! Is this a puzzle that you found elsewhere? If so, please edit where you found it into your question - we have an attribution policy here, and puzzles without sources may be closed & deleted. Dec 14, 2020 at 21:28
• So they only have to have one dwarf guess the number of marbles in one box correctly, right? Dec 14, 2020 at 22:49
• yes it is right Dec 14, 2020 at 23:05
• bilimgenc.tubitak.gov.tr/ayin-matematik-sorusu here is the original question.
– Oray
Dec 15, 2020 at 5:29
• and this is ongoing content.
– Oray
Dec 15, 2020 at 5:54