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YOU WILL HAVE TO SAY, "YOU WILL GIVE ME NEITHER COPPER NOR SILVER COIN." IF IT IS TRUE, THEN YOU WILL GET THE GOLD COIN. IF IT IS A LIE, THEN THE NEGATION MUST BE TRUE, SO THE STATEMENT BECOMES: "YOU WILL GIVE ME EITHER COPPER OR SILVER COIN". THIS WOULD BREAK THE GIVEN CONDITIONS THAT YOU GET NO COIN WHEN LYING. SO THE FIRST SENTENCE MUST BE TRUE THERE IS NO WAY TO GET AN AVERAGE SPEED OF 30 MPH (MILES PER HOUR). IF YOUR AVERAGE SPEED FOR THE 2 MILES STRETCH MUST BE 30 MPH, YOU SHOULD DO IT IN 4 MINUTES. DURING THE ASCENT, YOU WOULD HAVE ALREADY TAKEN 4 MINUTES TO TRAVEL 1 MILE AT 15 MPH. SINCE YOU HAVE TAKEN 4 MINUTES TO GO UP THE HILL, YOU WILL NEED TO TAKE 0 SECONDS TO TRAVEL THE 1 MILE DESCENT IN ORDER TO GET AN AVERAGE SPEED OF 30 MPH. THIS IS NOT POSSIBLE THERE ARE 99 RUNNERS IN MATT'S SCHOOL. THIS IS TRICKY. IF MATT IS THE FIFTIETH FASTEST RUNNER, HE WOULD BE NUMBER 50 IN THE SEQUENCE 1, 2, 3...50. TO BE THE FIFTIETH SLOWEST, HE'D HAVE TO BE NUMBER 50 IN THE SEQUENCE 50, 51, 52...99, SINCE THERE ARE FIFTY NUMBERS FROM 50 TO 99 INCLUSIVE 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