There are people who just scan for transactions which have the standard anyone can spend constructions (
OP_TRUE, in scriptPubKey or as p2sh) and just spend them. To avoid such people from discovering your transactions, you would have to use p2(w)sh with some other anyone can spend script which would have to be revealed as the prize. At that point, you might as well just use a normal p2(w)pkh script and make the prize the private key.
Additionally, anyone can spend scripts are non-standard and most wallet software do not have an easy way to create or spend transactions with anyone can spend scripts. If you have to provide hidden information as the prize, you might as well make that the private key.