Elf Hat Brainteaser

Once upon a time there were three elves who lived together in a small cottage. They always dressed in identical green tunics, however each wore a unique hat. The tallest elf always wore a red hat with white trim. The medium-sized elf always wore a purple hat with white trim,  and the smallest elf always wore a hat with yellow and green stripes. 

The three elves slept during the day, and got up after dark to make shoes for a poor shoemaker. One stormy night, rain blew through their window and extinguished their lantern. The elves didn’t have time to relight it. They got dressed in the dark and found their way to the shoemaker’s shop in the moonlight.  

When they got inside the shop, they lit the shoemaker’s lantern.

“Look,” said the medium-sized  elf. “We’re all wearing the wrong hats!”

“You’re right!” replied the elf wearing the yellow and green striped hat. 

What color hat did the tallest elf have on his head? 

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