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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 THE SHEEP WILL SURVIVE. IF THERE WERE 1 LION AND 1 SHEEP, THEN THE LION WOULD SIMPLY EAT THE SHEEP. THE SHEEP WILL NOT SURVIVE. IF THERE WERE 2 LIONS AND 1 SHEEP, THEN NO LION WOULD EAT THE SHEEP, BECAUSE IF ONE OF THEM WOULD, IT WOULD SURELY BE EATEN BY THE OTHER LION AFTERWARDS. THE SHEEP WILL SURVIVE. IF THERE WERE 3 LIONS AND 1 SHEEP, THEN ONE OF THE LIONS COULD SAFELY EAT THE SHEEP, BECAUSE IT WOULD TURN INTO THE SCENARIO WITH 2 LIONS, WHERE NO ONE CAN EAT THE SHEEP. THE SHEEP WILL NOT SURVIVE. IF THERE WERE 4 LIONS AND 1 SHEEP, THEN NO LION WOULD EAT THE SHEEP, BECAUSE IT WOULD TURN INTO THE SCENARIO WITH 3 LIONS. THE SHEEP WILL SURVIVE. CONTINUING THIS ARGUMENT, THE CONCLUSION IS AS FOLLOWS: IF THERE IS AN EVEN NUMBER OF LIONS, THEN NOTHING HAPPENS AND THE SHEEP SURVIVES. IF THERE IS AN ODD NUMBER OF LIONS, THEN ANY LION COULD SAFELY EAT THE SHEEP AND THE SHEEP WILL NOT SURVIVE. THIS IS SIMILAR TO THE UNEXPECTED HANGING PARADOX THE STUDENT IS DOUBLE COUNTING A LOT OF THE DAYS. A LOT OF THE TIME SPENT SLEEPING, EATING, AND RELAXING OCCURS DURING WEEKENDS AND THE SUMMER. WEEKENDS ALSO OCCUR DURING THE SUMMER, SO ALL OF THESE HOURS ARE GETTING COUNTED SEVERAL TIMES. AND, SCHOOL IS NOT AN ALL DAY AFFAIR. SO THE 4 DAYS ACTUALLY REPRESENTS MORE DAYS OF SCHOOL. IF SCHOOL IS 6 HOURS PER DAY, THOSE FOUR DAYS REPRESENTS 16 DAYS OF SCHOOL THERE MAY MANY POSSIBLE SOLUTIONS, HERE IS A SIMPLE ONE: THE FIRST PERSON TAKES HIS MONTHLY SALARY (LETS SAY $100), ADDS AN ARBITRARY AMOUNT THAT ONLY HE KNOWS (LETS SAY $475) AND WHISPERS THAT NUMBER ($575) TO THE SECOND PERSON. THE SECOND PERSON THEN ADDS HIS MONTHLY SALARY (LETS SAY $150) TO THAT VALUE AND WHISPERS THE NEW TOTAL ($725) TO THE THIRD PERSON. THE THIRD PERSON ADDS IN HIS SALARY, WHISPERS THE NEW TOTAL TO THE FOURTH PERSON AND SO ON UNTIL THE TENTH PERSON ADDS IN HIS SALARY AND WHISPERS THE FINAL TOTAL TO THE FIRST PERSON. THE FIRST PERSON THEN SUBTRACTS HIS ARBITRARY NUMBER FROM THAT TOTAL, DIVIDES BY 10, WHICH PRODUCES THE AVERAGE MONTHLY SALARY FOR THE GROUP WITHOUT ANYONE HAVING TO DIVULGE THEIR SALARY TO ANYONE ELSE