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YOU SHOULD GO FIRST, AND PUT A QUARTER AT THE EXACT CENTER OF THE TABLE. THEN, EACH TIME YOUR FRIEND PLACES A QUARTER DOWN, YOU SHOULD PLACE YOUR NEXT QUARTER IN THE SYMMETRIC POSITION ON THE OPPOSITE SIDE OF THE TABLE. THIS WILL ENSURE THAT YOU ALWAYS HAVE A PLACE TO PUT THE COIN, AND EVENTUALLY YOUR FRIEND WILL RUN OUT OF SPACE THE BIN WAS HALF FULL AT 10PM. THE SKIP STARTED WITH 1 LONELY BOTTLE. AT NOON: 1 PERSON CAME ALONG AND ADDED A BOTTLE, MAKING THE TOTAL 2 BOTTLES. AT 1PM: 2 PEOPLE CAME ALONG AND ADDED A BOTTLE EACH, MAKING THE TOTAL 2 + 2 = 4 BOTTLES. AT 2PM: 4 PEOPLE CAME ALONG AND ADDED A BOTTLE EACH, MAKING THE TOTAL 4 + 4 = 8 BOTTLES. AT 3PM: 8 PEOPLE CAME ALONG AND ADDED A BOTTLE EACH, MAKING THE TOTAL 8 + 8 = 16 BOTTLES. THEREFORE THE NUMBER OF BOTTLES IN THE BIN IS DOUBLING EVERY HOUR, AS IT WAS FULL AT 11PM, IT MUST HAVE BEEN HALF FULL AT 10PM THE THIEF IS THE SRI LANKAN SEAMAN. THEY ARE ON A JAPANESE SHIP, SO IT WILL BEAR A JAPANESE FLAG. THE JAPANESE FLAG WILL LOOK THE SAME UPSIDE DOWN PUT ONE BLUE MARBLE IN ONE JAR, AND PUT THE REST OF THE MARBLES IN THE OTHER JAR. THIS WILL GIVE YOU JUST ABOUT A 75% CHANCE OF PICKING A BLUE MARBLE. LET P(BLUE) = PROBABILITY OF PICKING A BLUE MARBLE. JAR 1 CONTAINS 1 BLUE MARBLE AND JAR 2 CONTAINS 99 BLUE MARBLES AND 100 RED MARBLES. SO: P(BLUE) = P(JAR 1) * P(BLUE IN JAR 1) + P(JAR 2) * P(BLUE IN JAR 2) P(BLUE) = 0.5 * 1 + 0.5 * 99/199 P(BLUE) = 0.748 THUS, WE END UP WITH ~75% CHANCE OF PICKING A BLUE MARBLE