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Can You Solve the Three Gods Riddle?

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In this TED-Ed riddle, we explore a classic logic puzzle invented by logician Raymond Smullyan. As the video tells us, it has been called the hardest logic puzzle ever. They're not kidding.

So here's the situation. You have crash-landed on a mysterious planet. The only way to escape is to appease three alien overlords (they were "gods" in the original telling, hence its name).

You know that the three aliens are named Tee, Eff, and Arr. There are also three artifacts on the planet, each of which matches a single alien (for the sake of simplicity, let's assume they are labeled "Tee," "Eff," and "Arr"). To appease the aliens, you need to match up the artifacts with their aliens—but you don't know which of the aliens is which!

You are allowed to ask three yes-or-no questions, each addressed to any one alien. (You can address multiple questions to the same alien, but you don't have to.)

To further complicate things, each alien has a specific behavior with regard to telling the truth. Tee's answers are always true. Eff's answers are always false. Arr's answers are random.

Yet another problem is that while you know the alien words "ozo" and "ulu" somehow correspond to "yes" and "no," but you don't know which is which. (I know, this situation just keeps getting worse!) So while you can communicate enough of the alien language to ask questions, they will respond only with "ozo" or "ulu." You may ask the questions one at a time, building on each response if you wish—meaning you have time to think about the next question based on what you have learned.

So your task is to ask three yes-or-no questions, while not knowing which answering words correspond to "yes" and "no," of three aliens whose identity is unknown, but whose behavior is predictable...if you knew their identity. How can you figure out which alien is which, so you can hand the right objects to the aliens? Put your thinking caps on, then roll the video explanation (which includes the answer, after a suitable pause):

For more on this puzzle, check out this TED-Ed page. For some flavor on logician Raymond Smullyan, check out his interview with Johnny Carson.

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A Simple Trick For Figuring Out the Day of the Week For Any Given Date
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People typically remember anniversaries in terms of dates and years, not days of the week. If you can’t remember whether you got married on a Saturday or Sunday, or don't know which day of the week you were born on, there’s a simple arithmetic-based math trick to help you figure out sans calendar, according to It's Okay To Be Smart host Joe Hanson.

Mathematician John Conway invented the so-called Doomsday Algorithm to calculate the day of the week for any date in history. It hinges on several sets of rules, including that a handful of certain dates always share the same day of the week, no matter what year it is. (Example: April 4, June 6, August 8, October 10, December 12, and the last day of February all fall on a Wednesday in 2018.) Using this day—called an “anchor day”—among other instructions, you can figure out, step by step, the very day of the week you’re searching for.

Learn more about the Doomsday Algorithm in the video below (and if it’s still stumping you, check out It’s OK to Be Smart’s handy cheat sheet here).

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A Man-Made Mountain in Finland Serves as an 11,000-Tree Time Capsule
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In 1982, the conceptual artist Agnes Denes set out to make a mountain. After a decade of work, she made it happen. In 1992, the Finnish government announced that it would sponsor Denes’s Tree Mountain—a 125-foot-tall manmade mountain built on top of a former gravel pit, designed to serve as part time capsule, part ecological recovery project.

Tree Mountain — A Living Time Capsule was constructed on the site of a former gravel pit near Ylöjärvi, Finland between 1992 and 1996. The artificially constructed landmass stands 125 feet tall, almost 1400 feet long, and more than 885 feet wide. (The top image of the triptych above shows the mountain in 1992 and the bottom image in 2013.) The forest planted on it forms a precise mathematical pattern Agnes designed based on the golden ratio-derived spirals of sunflowers and pineapples. From above, the oval mountain looks like a giant fingerprint made up of whorls of trees.

The project was never intended to just be aesthetically pleasing. Envisioned as a way to rehab land destroyed by mining, the trees are meant to develop undisturbed for 400 years, creating what will eventually be an Old Growth forest that can reduce erosion, provide wildlife habitats, and boost oxygen production.

And it was a communal effort. The roughly 11,000 pine trees were planted by different individuals who then became the custodians of those trees. Each received a certificate declaring their ownership for the project’s full term of 400 years. They can pass along this ownership to their descendants or to others for as many as 20 generations. These custodians (which include former UK prime minister John Major and former Icelandic president Vigdís Finnbogadóttir) are even allowed to be buried under their trees. But the trees can never be moved, and the mountain itself can’t be owned or sold off for those 400 years.

A triptych of images of Tree Mountain
Tree Mountain - A Living Time Capsule - 11,000 Trees, 11,000 People, 400 Years (Triptych) 1992-1996, 1992/2013
Copyright Agnes Denes, courtesy Leslie Tonkonow Artworks + Projects, New York

“Tree Mountain is the largest monument on earth that is international in scope, unparalleled in duration, and not dedicated to the human ego, but to benefit future generations with a meaningful legacy,” Denes writes. It “affirms humanity's commitment to the future well being of ecological, social and cultural life on the planet.”

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