13 writs or 13 vouchers? You need 13 writs as I understand. The amount of vouchers doesn't matter. Unsure but that's what I've seen on my end. Also why I gave up.
you need to complete thirteen (13) writs and deliver all thirteen (13) to the provision box. the number of unopened writs in your inventory does not matter, the amount of writ vouchers you have does not matter, the amount of anything else does not matter, all that matters is how many witch festival writs you have completed the quest for. Myself and many others have the hat and we only did 13.