BRATISLAVA MATHEMATICS CORRESPONDENCE SEMINAR
Faculty of Mathematics and Physics of Comenius University
Union of Slovak Mathematicians and Physicists
Centre of Spare Time - IUVENTA

BMCS - Problem set of the 1st fall series 1998/99

Logic

  1. Tina,Juro and Slavo are new members of BMCS organizers team. One of them writes the problem sets, another one corrects solutions and the last one carry out the administration. Corrector offered Writer some fresh oisters from Taiwan, but Writer prefers to eat caviar with Administrator. We know that Administrator eats more then Corrector and Slavo eats less then Tina. Tina have never heard about Slavo. Who is who in BMCS organizers team?

  2. Doc. Stuka tells Dr. Schwarz : "I see three persons coming into the school. The sum of their ages is equal to your age. And when we multiply their ages, we get number 2450." Dr. Schwarz answers that, that is not enough information to figure out their ages. So Doc. Stuka completes the information: "Anyone of them is not older then our chief. By the way, the age of every of these persons in years is bigger than number of points that your daughter achieved this year in Mathematics Olympiad".Now Dr. Schwarz knows the answer. How old is the chief?

  3. Michael thinks a word with 5 letters. He told you this word has some letters equal to following words. The number next to every given world shows how many letters are the same and on the same position as in Michaels word.
    PASTA -2; PANÁK -2; PRSTY -1; PLECE -1; DVERE -2; PADÁK -1
    What is the word that Michael thinks?

  4. From the pile of 27 oisters two players take alternate 1,2,3 or 4 oisters. The winner is, who has even number of oisters when there is no remaining oister in the pile. How many oisters should take the first player in first round, so he would definitely become the winner?

  5. Show, that every positive integer could be written as a sum of maximum 53 fourth powers of integers.

Problems in this series has been chosen by Misko Bajcsy and Alexander Erdelyi