There are cases where it’s obvious that it can’t be true (when seeing one or two modulo four red hats). In this case, assign 50 wizards to believe the number of red hats to be even and 50 wizards to believe they are odd. So 50 wizards will survive with 50% chance.

4) Assign 75 wizards to believe the number of hats is even, and 25 to believe the number of hats is odd.

5) I don’t think so. My best argument (there must be a better one) is that we have 2^100 different possible allocations, and 2/3 is not a multiple of 1/2^100, so we cannot choose an event that has exactly 2/3 probability.

6) Assuming n groups of wizards of size w_i who should survive with probability p_i, we have at least

sum(w_i*p_i) <= 0.5

p_i is a multiple of 1/2^100.

but probably there are more restrictions.

]]>Thank you for your comment. In Russian hat puzzles the word that is used is ‘mudrets’, which means wise man or sage.I do not actually know which word to use in English when I translate.

]]>Of course ,today one using this term mainly means some kind of magician (black or white magic,or how they call all these nonsense..)and not a wise man. In my mother-language (Greek) the ancient (Persian origin) word “magos” (Mάγος) which gave the Latin magus-magi and the modern magicienne(fr.) ,magician, e.t.c originally meant “wise man (of the east: Babylonian,Persian)” and not “Μagician”. This meaning is still existing in the linguistic tradition of the church, where the 3 wise men who brought gifts to baby Jesus are called the Magi (Οι Μάγοι).

Ι wonder if the difference in meaning exists also in other languages. For example I know the Russian маг (mag) of obvious etymology, and the word волшебник (balsέvnic). Perhaps Tanya,or some other Russian speaking friend could elaborate?

P.s Sorry for the irrelevant and highly unmathematical comment Tanya! 🙂 ]]>

May be, 75 wizards will survive with probability 1/3 and 25 wizards will be guaranteed ti survive?

]]>100+50 = 150 ??

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