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ANSWER: 15.

EXPLANATION: Let S1, S2, and S3 represent the number of coconuts taken by the first, second, and third sailor respectively and let X represent the number of coconuts in the original pile.

S1 = X/2 + 1/2

S2 = (X - S1)/2 + 1/2
S2 = ((X - (X/2 + 1/2)) /2) + 1/2
S2 = X/2 - (X/4 + 1/4) + 1/2
S2 = 2X/4 - (X/4 + 1/4) + 2/4
S2 = 2X/4 - X/4 - 1/4 + 2/4
S2 = X/4 + 1/4

S3 = (X - S1 - S2)/2 + 1/2
S3 = (X - (X/2 + 1/2) - (X/4 + 1/4))/2 + 1/2
S3 = X/2 - (X/4 + 1/4) - (X/8 + 1/8) + 1/2
S3 = X/2 - X/4 - 1/4 - X/8 - 1/8 + 1/2
S3 = 4X/8 - 2X/8 - 2/8 - X/8 - 1/8 + 4/8
S3 = X/8 + 1/8

X - S1 - S2 - S3 = 1
X - (X/2 + 1/2) - (X/4 + 1/4) - (X/8 + 1/8) = 1
X - X/2 - 1/2 - X/4 - 1/4 - X/8 - 1/8 = 1
8X/8 - 4X/8 - 4/8 - 2X/8 - 2/8 - X/8 - 1/8 = 1
X/8 - 7/8 = 1
X - 7 = 8
X = 15

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