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1) So I\'m watching \"Blockbusters\" last week and Bill said something to the effect that it was theoretically possible that you could have a game where every hexagon on the board can be claimed. Fact or crap and did that ever happen on the show?
2) When did \"Blockbusters\" go from the yellow set to the blue set?
3) I\'m trying a pinpoint a date here...Would anyone have a clue on when the \"Hevenly Hosts vs. Magnifecent M.C.\'s\" week of Dawson\'s Feud aired or taped? I know is that it was syndicated around \'83, but I\'m not sure about the month. If I had to guess....um, a sweeps month?
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I\'m pretty certain the answer to 1a is yes, it\'s theoretically possible, even if you assume both players play rationally and not pick meaningless hexes. It\'ll take somebody with a better knowledge of mathematical topology than I to explain. (It\'s trivial to use all 20 heses if the players play irrationally: have the family team go up and down the first four columns, followed by the solo player getting the first three in the last coulmn. The 20th hex will be the winning hex for either side.)
It\'s also a mathematical certainty that you can\'t have a draw. I don\'t think there were ever any games on Blockbusters that went the full 20 hexes.
I can\'t answer the other questions.
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I have an episode on tape where a game went (I think) 18 hexes. Solo player went three vertically from the top in the first and fifth columns and vertically from the bottom in the third. Family pair went from side to side, weaving around those blocks.
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It\'s also a mathematical certainty that you can\'t have a draw.
Did Nash\'s proof cover non-rhomboid boards, though? (I\'m gonna guess yes, since common sense dictates that the only way to keep one side from making their connection is to do so yourself, but I thought I would ask.)
But yes, since you (correctly) recognize that it\'s trivial to \"force\" the last-hex-wins situation, extrapolating from there I think you\'d find that it\'s not especially difficult (by changing a hex here and there) to come up with much more convoluted board layouts that set up the same condition. TPiRFan even points out (and I remember that game too, proving that I need to run Disk Cleanup on my brain and free that space up for something actually useful :)) that it\'s not especially difficult to set up that situation given alternating turns.
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I have an episode on tape where a game went (I think) 18 hexes. Solo player went three vertically from the top in the first and fifth columns and vertically from the bottom in the third. Family pair went from side to side, weaving around those blocks.
I lied. Sixteen hexes.
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Answer to #2 is early 1982 (not that far from the end of the series)
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Answer to #2 is early 1982 (not that far from the end of the series)
Actually, it was in November 1983 that the "GS hosts on Feud" week aired. I recall watching most of that week.
Cordially,
Tammy
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2) When did \"Blockbusters\" go from the yellow set to the blue set?
March 1, 1982. GSN started with 2/1/82, so we have a few weeks to go before we see it.
Personally I thought the blue looked a thousand times nicer...wish they had went with it earlier.
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Answer to #2 is early 1982 (not that far from the end of the series)
Actually, it was in November 1983 that the \"GS hosts on Feud\" week aired. I recall watching most of that week.
He\'s referring to question 2, which is about \"Blockbusters\".
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It would be easy to brute-force it; just draw out the hexes, grab some markers of whatever kind (pennies and nickels, colored chips) and move \'em around.
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It\'s certainly mathematically possible to have a board layout where 19 spaces are filled and the 20th will determine the winner (quick example here), but it seems like it would be unlikely to get there unless someone picked some spaces that were of very little or no strategic help to them.
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After a bit of trial and error, I came up with this hypothetical game in which both players play rationally and all 20 spaces are necessary. The colors are of course who wins each space, and the numbers are the order in which the spaces are taken, with the green space being #20.
Sorry for the quality, but it was the best I could do with a quick and dirty use of MS Paint.
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Wow, good work! Seems completely plausible to me as well.
