what's wrong with this picture then...http://www.sucs.org/~crystal/solution.phpAs this particular version is worded, N prisoners will eventually visit the room N times each, which is all well and good, except that freedom is not claimed until ~2N visits.
In the *original version, no N-visit constraints are imposed. Nonetheless, on average, each prisoner will visit the switch room once per successful spokesman 'count'. (This assumption uses a linear model to predict successful non-spokesman visits, which in reality will be exponential, thus greatly increasing the figures used herein.) Thus, 23x44 = 1012 visits are required - a mere 2 years, 282 days, assuming daily visits. However, "from time to time" imples, to me, a maximum of weekly visits, and significant periods of non-visitage. Thus 19 years, 144 days (assuming 5 leap years) will elapse, on average, before freedom is to be claimed. Any solution which relies on the ability of all 23 prisoners to maintain their sanity over 2 years in isolation, let alone 19 years, must surely be doomed to failure, regardless of the mathematical correctness. The prisoners would do much better simply rushing the warden and guards there and then - the only time they will all be together.
