Shh, don't tell: the full text is now at http://people.brandeis.edu/~kleber/priv/zram.pdf The relevant bit is pp.15-17. There are six positions which require exactly 80 moves to solve, and that's maximal. This paper just reports on the results; the work is really done, it seems, in Brungger's ETH Ph.D. thesis, which somehow I haven't found on-line. (An earlier ETH thesis found four of the remoteness 80 positions, with proof, and also proved no position had remoteness more than 87.) On Tuesday, November 11, 2003, at 08:25 AM, N. J. A. Sloane wrote:
Patric.Ostergard@hut.fi writes as follows:
a(4)=80. This has been shown in A. Br\"ungger, A. Marzetta, K. Fukuda & J. Nievergelt, The parallel search bench ZRAM and its applications, Annals of Operations Research 90 (1999), 45--63.
NJAS
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--Michael Kleber kleber@brandeis.edu