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I called P&O to verify ages and the girl told me it was 21 as the age limit.
"Please note that Arcadia and Artemis are dedicated to adults and therefore we do not accept children or teenagers under the age of 18" The following is taken from the P&O website under the 'what is available for families section'. Sounds like what they say on the phone isn't consistent with the website.
We find if it's a ship that caters for 'adults only' the majority of people on board are quite elderly and the ship doesn't have the sort of entertainment that would cater for 18 year olds. You would probably be better looking into a short cruise on the Oceana which is a child friendly ship for teenagers as well as young adults and older guests. We went on a short trip to Bruges on the Aurora and were very pleased what they offer for a short 'party cruise'. We are going to try the Oceana though as we have a 50th Anniversary in 2010 and want to take the grandchildren ageing from 4 years to 22 the PO Oceana will probably be a safer bet for all ages. Good luck.
I went on a 2 night mini-cruise to Bruges on Arcadia in May 2007. It was the same weekend as the FA Cup Final, so warnings that we had that the ship may be full of stag parties proved unfounded. The passenger complement was actually quite young with lots of hen, birthday and anniversary parties on board. I reckon the average age was around 35 with lots of young adults on board. My experience of these 2 night cruises is that they are mainly taken up by the party set who are happy to stay up all night. You can't do that so easily with children in tow! P&O often have popular entertainers on Arcadia (such as Brian Conley) for the two night party cruises. Our experience was enjoyable and good fun.