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A074894
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Full list of counterexamples for the k=3 version of the malicious apprentice problem.
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1
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OFFSET
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1,1
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COMMENTS
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This is the problem of the farmer's helper who, when asked to weigh n bags of grain, does so k at a time and reports the resulting binomial(n,k) combined weights with no indication of the k-tuples that produced them. The problem: is can the weights of the bags be recovered?
For k=3 the answer is Yes unless n is one of the four terms of this sequence. For k=2 see A057716.
The old entry with this sequence number was a duplicate of A030109.
The following references also apply to the general case of the problem.
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REFERENCES
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W. W. Rouse Ball, A Short Account of the History of Mathematics.
E. Bolker, The finite Radon transform, Contemp. Math., 63 (1987) 27-50.
R. K. Guy, Unsolved Problems in Number Theory, C5.
Ross A. Honsberger, A gem from combinatorics, Bull. ICA, 1 (1991) 56-58.
B. Liu and X. Zhang, On harmonious labelings of graphs, Ars Combin., 36 (1993) 315-326.
J. Ossowski, On a problem of Galvin, Congressus Numerantium, 96 (1993) 65-74.
P. Winkler, Mathematical Mind-Benders, Peters, Wellesley, MA, 2007; see p. 27.
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LINKS
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L. Moser and C. F. Pinzka, Problem E1248, Amer. Math. Monthly, 64 (1957) 507.
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EXAMPLE
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For n=27 Boman and Linusson give five examples of which the simplest is {-4,-1^{10},2^{16}} and its negative, where exponents denote repetitions. For n=486 Boman and Linusson give {-7,-4^{56},-1^{231},2^{176},5^{22}} and its negative.
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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