

A074894


Full list of counterexamples for the k=3 version of the malicious apprentice problem.


1




OFFSET

1,1


COMMENTS

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 ktuples 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.


REFERENCES

W. W. Rouse Ball, A Short Account of the History of Mathematics.
E. Bolker, The finite Radon transform, Contemp. Math., 63 (1987) 2750.
R. K. Guy, Unsolved Problems in Number Theory, C5.
Ross A. Honsberger, A gem from combinatorics, Bull. ICA, 1 (1991) 5658.
B. Liu and X. Zhang, On harmonious labelings of graphs, Ars Combin., 36 (1993) 315326.
J. Ossowski, On a problem of Galvin, Congressus Numerantium, 96 (1993) 6574.
P. Winkler, Mathematical MindBenders, Peters, Wellesley, MA, 2007; see p. 27.


LINKS

Table of n, a(n) for n=1..4.
I. N. Baker, Solutions of the functional equation (f(x))^2f(x^2)=h(x), Canad. Math. Bull., 3 (1960) 113120.
J. Boman, E. Bolker and P. O'Neil, The combinatorial Radon transform modulo the symmetric group, Adv. Appl. Math., 12 (1991) 400411.
Jan Boman and Svante Linusson, Examples of nonuniqueness for the combinatorial Radon transform modulo the symmetric group, Math. Scand. 78 (1996), 207212.
John A. Ewell, On the determination of sets by sets of sums of fixed order, Canad. J. Math., 20 (1968) 596611.
B. Gordon, A. S. Fraenkel and E. G. Straus, On the determination of sets by the sets of sums of a certain order, Pacific J. Math., 12 (1962) 187196.
J. Lambek and L. Moser, On some two way classifications of the integers, Canad. Math. Bull., 2 (1959) 8589.
L. Moser and C. F. Pinzka, Problem E1248, Amer. Math. Monthly, 64 (1957) 507.
D. G. Rogers, A functional equation: solution to Problem 8919, SIAM Review, 32 (1990) 684686.
J. L. Selfridge and E. G. Straus, On the determination of numbers by their sums of a fixed order, Pacific J. Math., 8 (1958) 847856.


EXAMPLE

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.


CROSSREFS

See A057716 for the case k=2.
Sequence in context: A270889 A097678 A251609 * A287881 A287883 A246753
Adjacent sequences: A074891 A074892 A074893 * A074895 A074896 A074897


KEYWORD

nonn,fini,full


AUTHOR

N. J. A. Sloane, based on email from R. K. Guy, Oct 30 2008


STATUS

approved



