Date: 2007-07-23 03:59 pm (UTC)
(none =1 or >4; at most two 2s; a most one 4; can't have both 2 and 4)

More concisely: since 2+2 = 2*2, you can ignore 4 as well, so you're left with just 2s and 3s, and at most two 2s. (We're only after the biggest total, not the number of ways of writing it!)
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