What colour is your bandana?

One night at camp when I joined the group at the fire, everyone in the family was discussing a riddle that only Boy in Black and With-a-Why knew how to solve. Boy in Black had learned it from his friend MathKid, who claimed that students at his college of Most Impressive Technology had made it up, although some of us suspect it's one of those brain teasers that's been around for a while and resurfaces in different forms.

Here's the riddle: An Evil Ruler has 100 gnomes. She lines them up in a straight line on a hill, so that each gnome can see all the gnomes ahead of him, but none of the gnomes behind him. She has 100 blue hats and 100 red hats. She puts a hat on each of the gnomes. A gnome cannot see his own hat -- or any of the hats behind him -- but he can see the hats of the gnomes ahead of him. He can hear what is happening behind him, but he cannot turn back and look.

Starting with the very last gnome in line, the Evil Ruler asks, "What colour is your hat?" The gnome is allowed to say one word, either "blue" or "red." If the prisoner answers correctly, he is allowed to live. If he says the wrong answer, he is killed. Then the Evil Ruler goes onto the next gnome.

The gnomes are given time to make a plan before this fun game begins. The Evil Ruler can hear them talking so it's not a secret plan. They cannot change any of the rules. Once the game begins, they cannot talk, except to answer the evil ruler. Each gnome must answer the Evil Ruler with one of two words, red or blue, and they may not signal anything with gestures or voice inflection.

Using logic, they come up with a plan that will save at least 99 of the 100 gnomes. What is the plan?

We all kept discussing this riddle at the fire, everyone talking at once and jumping in with ideas and arguing about the plan. Some family members got bored and went off to play cards or go to sleep, while others were obsessed with figuring out the answer. We quickly dropped the number of gnomes from 100 to ten, figuring that any plan that worked for ten would work for 100. I got playing cards, ten of them, some red and some black, and laid them on the bench to try to figure out the answer, a strategy which perhaps would have helped had it been light enough to see the cards.

Shaggy Hair Boy was the first to come up with an answer. He disappeared into the darkness with Boy in Black, and they returned to the fire, with Boy in Black saying, "Yep, he's got it," and Shaggy Hair smiling smugly. Naturally, he did not tell any of us the answer.

It wasn't until I'd left the campfire and was lying in the quiet darkness of the small tent I share with my husband that I came up with the answer to the riddle. I pushed my husband aside, threw off the old quilt we use as a blanket, put my clothes and sneakers back on, unzipped the tent, and went racing off across the field to the big tent where all the kids sleep so that I could make Boy in Black come out and hear my answer.

I returned to the tent, carefully zipping the nylon door behind me and tossing off the sneakers now wet from running across the dewy field. "I got it!" I exclaimed triumphantly to my husband.

"No, you aren't obsessive at all," he muttered.

The next day at breakfast, family members who hadn't been at the fire had to hear the riddle. You could tell which ones were determined to figure it out. They were the ones drawing little diagrams on paper plates, or staring at ten cards spread out on the ground, muttering under their breath. I could tell when Blonde Niece figured out the answer, just from the look on her face. Schoolteacher Niece jumped up and down when she got it.

Later that morning, we attempted to act out the riddle, using black and red bandanas put randomly on ten family members. With-a-Why posed as the Evil Ruler.



The gnomes include my mother, my brother, my oldest sister, my youngest sister, three of my kids, and three of my nieces. Ignore the crazy gestures in the top photo. Hand signals are not allowed. The group kept breaking into the song YMCA, even though that was not part of the riddle at all.