Rock Paper Scissors

You are on your way to the Farmer’s Market to buy some cheese, but you are running late. You know the best cheese will be gone if you don’t get there early, so you decide to take the shortcut through the woods and over the bridge.

Unfortunately, the bridge is guarded by a troll who won’t let you pass unless you solve a riddle. Fortunately, you’ve solved his riddles before so you feel pretty confident.

When you get to the bridge, the Troll blocks your way. He tells you he won’t let you reach the other side unless you give him a bag of gold.

You don’t have a bag of gold.

“Can’t I just solve a riddle?” you ask.

“You are too good at riddles.” replies the Troll.

“How about a game of Rock, Paper, Scissors? If I win, you have to let me pass.” you suggest.

“Best out of ten games. If I win, I get to throw you in the river.” replies the Troll

In the classic game, Rock, Paper Scissors, rock beats scissors, paper beats rock, and scissors beats paper. You are pretty sure the Troll will choose rock every time. You agree to play ten games.

As you expected, the Troll chooses rock in the first three games. You choose paper, so you are ahead: 3 games to 0.

But then the Troll catches on. In the next seven games, he mixes it up. At the end of ten games, the Troll has used rock 3 times, paper 4 times and scissors 3 times. You have used rock 3 times, paper 5 times, and scissors twice. No game ends in a tie.

How many games did the Troll win? Does he get to throw you in the river?

Hint: Did you do the Elf Brainteaser? You can figure this out the same way!