Purposefully, purposely and even purposively. It's a tricky area and the meanings can overlap.
I'm inclined to agree with Paul because if I do something purposefully, then I'm doing it in order to achieve something. I have a goal in mind. At least that's how I see it but others may disagree. The party was simply an end in itself so they weren't doing anything purposefully.
On another matter, I wish the BBC on Radio 3 would not refer to 16th April as Easter Saturday. If it's anything, it's Holy Saturday. Easter begins this Sunday so Easter Saturday comes after that, on the 23rd.