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Pyne, who has been fighting Hodgkin's lymphoma for the past four years, said her goals include swimming with sharks, entering her dog Mabel in a dog show, meeting pop band Take That and encouraging people to donate bone marrow.
"I've been fighting cancer for almost 4 years now and I know the cancer is gaining on me and it doesn't look like I'm going to win this one," the teenager wrote on her blog. "Mum always tells me that life is what we make of it and so I'm going to make the best of what I have and because there were so many things I still wanted to do."
The re-tweets, featuring the hash tag #alicebucketlist, spread to thousands of Twitter users and made the list one of the top trends on Twitter Wednesday.