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A bit of spherical geometry says all Messiers are visible to 20.3 deg S.
Someone might like to recheck the math but:
M82 goes at a line through Port Headland WA and Hamilton Island Qld
M81 - line Mount Potter WA and Homestead Bay Qld
M52 - line Kaburie WA and Braeside Qld
M103 - line Mount Misery WA and Banyabba Railway Station NSW
Since the gaps after that aren't big:
M40, M102, M108 and M97 - line Flinders Park WA and Warrain Beach NSW
M101, M109 and M76 - don't survive Victoria
M39, M106, M51, M92, M34, M63, M110, M31, M94, M32, M29, M13 and M38 - disappear in that order over Tasmania
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