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Date: 22-12-2020
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Date: 19-1-2021
680
Date: 23-8-2020
562
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Pick two real numbers and at random in with a uniform distribution. What is the probability that , where denotes the nearest integer function, is even?
The answer may be found as follows.
(1) |
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(2) |
so
(3) |
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(4) |
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(5) |
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(6) |
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(7) |
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(8) |
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(9) |
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(10) |
(OEIS A091651).
REFERENCES:
American Mathematics Competitions. Problem B3 in "William Lowell Putnam Competition Archive, 1993" https://www.unl.edu/amc/a-activities/a7-problems/putnam/.
Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, p. 139, 2003.
Losinski, L. F.; Alexanderson, G. L.; and Larson, L. C. "The Fifty-Fourth William Lowell Putnam Mathematical Competition." Amer. Math. Monthly 101, 725-734, 1994.
Scholes, J. "54th Putnam 1993." https://www.kalva.demon.co.uk/putnam/putn93.html.
Sloane, N. J. A. Sequence A091651 in "The On-Line Encyclopedia of Integer Sequences."
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