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Das Problem der Abzählreime und Zahlentwicklungen mit gebrochenen Basen. (The problem of counting-out rhymes and expansion of numbers into fractional bases). (German) Zbl 0622.10005

Es werden Resultate über die Entwicklung natürlicher Zahlen nach gebrochenen Basen r/s \((r>s\), r,s teilerfremd) bewiesen und diese auf Probleme angewendet, die sich populär in der Frage nach der letzten verbleibenden von n Personen bei Anwendung eines k-silbigen Abzählreims formulieren lassen.
Reviewer: P.Kirschenhofer

MSC:

11A63 Radix representation; digital problems
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References:

[1] Eggan, L. C.; Vanden Eynden, C. L., “Decimal” expansions to nonintegral bases, Amer. Math. Monthly, 73 (1966) · Zbl 0138.03402
[2] Gardner, M., Kopf oder Zahl (1978), Weinheim
[3] Kobert, H., On quasi-decimals and on arithmetical properties of certain perfect sets and monotone functions, J. London Math. Soc., 28 (1953) · Zbl 0050.27705
[4] Schubert, H., Zwölf Geduldsspiele (1895), Berlin
[5] Schuh, F., (The Master Book of Mathematical Recreation (1968), Dover: Dover New York), Sects. 298-301 · Zbl 0191.27406
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