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B _ T T _ R _ _ S Clue
YOU WILL NEED A MAXIMUM OF 7 ATTEMPTS TO FIND 2 WORKING BATTERIES. BREAK THE BATTERIES INTO 3 GROUPS: TWO GROUPS OF 3 AND ONE GROUP OF 2. BY DOING THIS YOU GUARANTEE THAT AT LEAST ONE OF THE GROUPS HAS 2 WORKING BATTERIES. BOTH OF THE GROUPS OF 3 HAVE 3 POSSIBLE COMBINATIONS OF 2 BATTERIES AND THE GROUP OF 2 ONLY HAS 1 COMBINATION. SO, 3 + 3 + 1 = 7 TRIES AT MOST TO FIND TWO WORKING BATTERIES YOU WILL NEED TO MAKE THREE CUTS. CUT ALL THREE LINKS ON ONE CHAIN AND SEPARATE THEM. NOW YOU HAVE 3 CHAINS AND 3 LINKS. THEN, USE THESE 3 INDIVIDUAL LINKS TO JOIN THE OTHER THREE CHAINS TOGETHER ZOE'S SMALLEST POSSIBLE NUMBER IS 6. BASED ON THE FIRST STATEMENT OF ALI, IT INDICATES THAT HE HAS NEITHER 1 NOR 9. IF HE HAD EITHER 1 OR 9 THEN HE WOULD KNOW THAT ZOE MUST HAVE A BIGGER OR SMALLER NUMBER. NOW ZOE, BASED ON ALI'S FIRST STATEMENT, KNOWS THAT ALI DOESN'T HAVE 1 OR 9. ZOE'S FIRST STATEMENT INDICATES THAT SHE DOES NOT HAVE 2 OR 8 (NEITHER 1 NOR 9). IF SHE HAD 1, 2, 8 OR 9, THEN SHE COULD HAVE CONCLUDED THAT ALI HAS A BIGGER OR SMALLER NUMBER. NOW ALI KNOWS THAT ZOE DOESN'T HAVE 1, 2, 8 OR 9. ALI'S SECOND STATEMENT INDICATES THAT HE DOES NOT HAVE 3 OR 7 AND ALSO NOT 1, 2, 8 OR 9. ZONE CAN CONCLUDE THAT ALI DOESN'T HAVE 1, 2, 3, 7, 8 OR 9. IN SHORT, ALI MUST HAVE EITHER 4, 5 OR 6. NOW WHEN ZOE SAYS THAT SHE HAS A BIGGER NUMBER THEN IT MUST BE EITHER 6, 7, 8 OR 9 AND ALI HAVING 4 OR 5. ZOE CAN'T SAY CONFIDENTLY THAT SHE HAS A BIGGER NUMBER IF SHE HAD A 4 OR 5, AS IT COULD BE SMALLER THAN WHAT ALI COULD HAVE. SO ZOE'S SMALLEST POSSIBLE NUMBER IS A 6 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