Before this trip, I did not know this Australian phrase. One of the people on our tour, Wayne, said it all the time, but it wasn't until Dee brought it up that I started hearing it. "Fair dinkum" (imagine it with a strong Aussie accent) is used to express surprise at something the speaker has said, along the lines of "Really", but less a question and more an exclamation. Rarely, it can also be used as an adjective meaning "real". Apparently, it's generally older Australian men, generally more from the country than the city, that use it. None of the younger Aussies on the trip used it, and they said they would probably be mocked if they did, but they all knew what it meant. Wayne liked to tell and hear stories, and after any sufficiently surprising one, he would counter with a hearty "fair dinkum".
I looked up the origin, and as with many things like this, there are several theories, some of which have been disproven. One popular one says that it originates from the Chinese "din gum", meaning "real gold". Another says it's a corruption of "fair drinking" from the convict days. Most dictionaries just say "origin unknown".
Among Rob, Michelle, Dennise and me, it became kind of a joke how often Wayne said "fair dinkum", and we sometimes even tried to elicit one with a particularly amazing story. Near the end of the Vietnam trip, Rob said he was surprised I hadn't made a bet to try to win my money back from the train bet. We decided that the four of us would all put in $5 and guess how many times Wayne would say "fair dinkum" in the 6 days we would be in Cambodia, the money going to the person with the closest guess. Michelle and I both guessed 42, so Michelle upped her guess to 45. Rob and Dee were more optimistic, guessing 59 and 60 respectively. Stay tuned for the result.