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The number of ways of grading examination candidates

  • W. T. Tutte and Cedric A. B. Smith

Extract

Candidates are graded by their examination results in some such way as 1st B; 2nd equal A, D; 4th equal C, E; and so on. In how many ways gn can n candidates be graded? This problem was solved by Cayley [1, pp. 374-378] and later by others. It does not seem to be well known, and the following result may be of interest.

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1. Cayley, A., On the theory of the analytical forms called trees, II. Phil. Mag. 18 (1859).
2. Sloane, N. J. A. and Plouffe, Simon, The encyclopedia of integer sequences, Academic Press (1995).

The number of ways of grading examination candidates

  • W. T. Tutte and Cedric A. B. Smith

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