5 0
S T _ T _ M _ N T S
_ R _
C _ R R _ C T
_ N D
5 0
_ R _
_ N C _ R R _ C T .
S T _ T _ M _ N T S
1
T _
5 0
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T R _ _
_ N D
S T _ T _ M _ N T S
5 1
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1 0 0
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I F
_ N Y
_ N _
_ F
T H _
S T _ T _ M _ N T S
_ S
T R _ _ ,
T H _ N
_ L L
_ F
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S T _ T _ M _ N T S
N _ M B _ R _ D
L _ W _ R
T H _ N
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M _ S T
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B _
T R _ _ ,
B _ C _ _ S _
T H _
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" _ T
L _ _ S T "
_ S
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_ F
_
F _ W _ R
N _ M B _ R ,
_ N D
T H _ Y
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_ N
_ S C _ N D _ N G
_ R D _ R .
A S S _ M _ N G
S T _ T _ M _ N T
1
_ S
T R _ _ ;
T H _ N
S T _ T _ M _ N T
1 0 0
_ S
F _ L S _ .
A S S _ M _ N G
S T _ T _ M _ N T S
1 - 2
_ R _
T R _ _ ;
T H _ N
S T _ T _ M _ N T S
9 9 - 1 0 0
_ R _
F _ L S _ .
A S S _ M _ N G
S T _ T _ M _ N T S
1 - 3
_ R _
T R _ _ ;
T H _ N
S T _ T _ M _ N T S
9 8 - 1 0 0
_ R _
F _ L S _ .
A S S _ M _ N G
S T _ T _ M _ N T S
1 - 4
_ R _
T R _ _ ;
T H _ N
S T _ T _ M _ N T S
9 7 - 1 0 0
_ R _
F _ L S _ .
. . .
A S S _ M _ N G
S T _ T _ M _ N T S
1 - 5 0
_ R _
T R _ _ ;
T H _ N
S T _ T _ M _ N T S
5 1 - 1 0 0
_ R _
F _ L S _ .
S T _ T _ M _ N T
9 9
W _ L L
B _
T H _
_ N L Y
C _ R R _ C T
S T _ T _ M _ N T
_ F
T H _
T _ R M S
" _ T
L _ _ S T "
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R _ P L _ C _ D
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" _ X _ C T L Y . " ,
_ . G .
" E X _ C T L Y
9 9
_ F
T H _ S _
S T _ T _ M _ N T S
_ R _
F _ L S _ . " Clue
50 STATEMENTS ARE CORRECT AND 50 ARE INCORRECT. STATEMENTS 1 TO 50 ARE TRUE AND STATEMENTS 51 TO 100 ARE FALSE. IF ANY ONE OF THE STATEMENTS IS TRUE, THEN ALL OF THE STATEMENTS NUMBERED LOWER THAN THAT ONE MUST ALSO BE TRUE, BECAUSE THE TERM "AT LEAST" IS INCLUSIVE OF A FEWER NUMBER, AND THEY ARE NUMBERED IN ASCENDING ORDER. ASSUMING STATEMENT 1 IS TRUE; THEN STATEMENT 100 IS FALSE. ASSUMING STATEMENTS 1-2 ARE TRUE; THEN STATEMENTS 99-100 ARE FALSE. ASSUMING STATEMENTS 1-3 ARE TRUE; THEN STATEMENTS 98-100 ARE FALSE. ASSUMING STATEMENTS 1-4 ARE TRUE; THEN STATEMENTS 97-100 ARE FALSE. ... ASSUMING STATEMENTS 1-50 ARE TRUE; THEN STATEMENTS 51-100 ARE FALSE. STATEMENT 99 WILL BE THE ONLY CORRECT STATEMENT IF THE TERMS "AT LEAST" ARE REPLACED WITH THE TERM "EXACTLY.", E.G. "EXACTLY 99 OF THESE STATEMENTS ARE FALSE." HE WILL HAVE 25 COCONUTS WITH HIM AT THE END. THE TRICK IS TO REDUCE THE NUMBER OF SACKS AS YOU PASS CHECKPOINTS. THE FIRST 10 CHECKPOINTS REQUIRE 3 COCONUTS EACH, WHICH EMPTIES HIS FIRST SACK. THE NEXT 15 CHECKPOINTS REQUIRE 2 COCONUTS EACH, WHICH WILL EMPTY HIS SECOND STACK. NOW, HE IS LEFT WITH 1 SACK AND 5 MORE CHECKPOINTS. SO, THE 5 CHECKPOINTS WILL TAKE 1 COCONUT EACH. THEREFORE, HE WILL BE LEFT WITH 25 COCONUTS 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 THE MINIMUM NUMBER OF WEIGHTS REQUIRED IS FIVE AND THESE SHOULD WEIGHT 1, 3, 9, 27 AND 81 POUNDS. THE MERCHANT HAS TO USE A BALANCE WEIGHING SCALE TO DO THE JOB. TO WEIGH 2 POUNDS, HE'LL HAVE TO PUT THE 3 POUND WEIGHT ON ONE PAN AND 1 POUND WEIGHT ON THE OTHER PAN. TO WEIGH 5 POUNDS, HE'LL HAVE TO PUT THE 9 POUND WEIGHT ON ONE PAN AND 1 AND 3 POUND WEIGHTS ON THE OTHER PAN