You and your friend find a great new sticker set on the Signal app. The set has 11 stickers; you and your friend want to send them to each other without sending the same one twice. You first send 1, 2, or 3 stickers to your friend. Your friend then sends you 1, 2, or 3 sticks, and so on.

Riddle 1: Can you send the right amount of stickers per turn so that you always send the final sticker to complete the set of 11? If so, how many stickers do you send with your first message?

Riddle 2: Can you ensure that you send the final sticker if there was a set of 30 instead of 11? If so, how many stickers do you send with your first message?

Riddle 3: Can you send the final sticker in general, with n stickers to be sent 1-to-p at a time (p is not greater than n)? If so, how many stickers do you send with your first message?

Can you be the first to solve three riddles? Post your answer here and note which riddle you’re answering in your reply. Satoshi would be proud!

Riddle 1
Send 3 with first message. Then, make sure the number of stickers you send is 4 minus number of stickers your friend last sent, you will win in two rounds.

Riddle 2
Yes, send 2 stickers with first message and follow the same strategy.

Riddle 3
Yes, send n % 4 stickers in the first message, then p where p is 4 - o each turn where o was opponent’s last turn.