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Infinity is one of those concepts that we think we understand, but most (all?) of us can't actually wrap our minds around. German mathematician David Hilbert created a thought experiment called the "Grand Hotel paradox" to demonstrate the absurd complexity of infinity.

In this thought experiment, you're responsible for managing a grand hotel with a countably infinite number of rooms, all of which have guests in them. As finite and infinite groups of new guests arrive, you need to figure out schemes to fit them into rooms without displacing the infinite number of existing guests who are already in rooms. This turns out to involve a really clever—and difficult—set of math tricks.

In this TED-Ed lesson, Jeff Dekofsky walks you through the process, and may cause your brain to explode along the way. Have fun:

For more on this, check out the TED-Ed lesson page or the surprisingly good Wikipedia entry on the paradox.

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Prepare to Be Stumped By This Math Problem Meant for Fifth Graders
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Math is hard. Just ask Mumsnet user PeerieBreeks, who posted a ‘simple’ math riddle meant for fifth graders to the parenting website, and ended up with more than 500 comments—many of them from adults struggling to come up with the correct answer. Here’s the riddle:

For the most part, the problem-solvers who shared their answers all believed that the man made a profit, but whether it was \$10, \$20, or \$30 seemed to be in hot dispute. Can you figure it out? (Scroll down for the answer. We’ll give you a minute …)

The wording of the riddle, not the math, seems to be what’s throwing most people off. Because the transactions in question relate to the same horse, people are looking at it as a single, four-part transaction—buys, sells, buys, sells. But the correct way to look at the problem, and figure out the answer, is to look at it as just two transactions: a man bought a horse and sold a horse. A man bought a horse and sold a horse. (The man could just as easily have bought and sold a dog in one of those transactions and it wouldn’t change the outcome.)

All of which is to say that the correct answer is: The man made a \$20 profit.

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March 14, the mathematic high holiday known as Pi Day, is right around the corner. To celebrate everyone's favorite irrational number, we've rounded up some gifts to help the math aficionados in your life—the ones who know that pi is the ratio of the circumference of a circle to its diameter—observe Pi Day in proper fashion.

Mental Floss has affiliate relationships with certain retailers and may receive a small percentage of any sale. But we only get commission on items you buy and don't return, so we're only happy if you're happy. Thanks for helping us pay the bills!

#### 1. PI PIE PAN; \$25

If Pi Day passed and you didn't eat a pi pie, did Pi Day even happen? This specially shaped baking pan makes the equivalent volume of a 9-inch round pan, but obviously has more surface area than a standard pan. Pi puns and extra crust? Sounds like a win-win dessert.

Find It: Amazon

#### 2. "I EIGHT SUM PI PLATES"; \$35

Pair that pi pie with a set of these special plates decorated with a formula that spells out "imaginary unit eight summation pi"—or, essentially, "I ate some pie." Yes please!

Find It: Uncommon Goods

#### 3. CUTIE PI UNISEX ONESIE; \$14

Inspire a love of irrational numbers in the young mathematician-to-be in your life with this adorable cotton onesie, available in five colors for 6-24 month olds.

Find It: Etsy

#### 4. CHEAT SHEET SHOWER CURTAIN; \$69

We do our best thinking in the shower, and this machine-washable shower curtain is sure to inspire a stumped mathematician to finally figure out x once and for all.

Find It: Society6

#### 5. PI MIRRORS PIE T-SHIRT; \$6

Consider this equation: Math puns + affordability = this hilarious gift tee.

Find It: \$6 Dollar Shirts

#### 6. MATHEMATICAL GLASSES; \$38

You'll be toasting to a gift well done after they open this set of four pint glasses measuring out the number of ounces in Pythagoras's constant, the Golden Ratio, Euler's Number, and of course pi.

Find It: Uncommon Goods

#### 7. QUANTUM PHYSICS FOR BABIES; \$7

It's never too early to get your budding mathematician hooked on STEM! This quantum physics intro is meant for 1–3 year olds, but it's a good refresher for adults to brush up on their knowledge too.

Find It: Amazon

#### 8. SPIRAL PI TATTOO; \$12

This "classroom pack" of temporary tattoos means that when you and 44 of your closest pi pals practice memorizing pi's numerous digits, you never have to leave home without your cheat sheet.

Find It: Amazon

#### 9. ALBERT CLOCK; \$340

Definitely know your audience before gifting this head-scratcher of a clock. For some, the regular mental exercise to figure out the time would be a welcomed brain-teaser. For others, it could be a frustrating distraction. But, we think its namesake—it should be relatively easy to figure out which Albert it's referencing—would be a fan.

Find It: Museum of Modern Art

#### 10. MATHEMATICS LEGGINGS; \$25

Spend your savasana meditating on the wonders of math in these equation-covered leggings, which come in sizes XS-4X.

Find It: Modcloth

#### 11. ADD AND SUBTRACT ABACUS; \$20

Ancient calculators make great toys when it comes to this colorful bead toy aimed at kids 2 and up. But once the young ones hit grade school, this specially marked abacus will help them visualize arithmetic while still seeing the equations listed out.

Find It: Amazon

#### 12. PATTERNS OF THE UNIVERSE COLORING BOOK; \$13

This coloring book takes nature's best mathematical patterns and turns them into a soothing adult coloring book. Take a break from studying math's interconnected worlds, and just connect pencil to paper for a bit.

Find It: Target

#### 13. PI SIGN COOKIE CUTTERS; STARTING AT \$5

Cookies are certainly easier to bake in bulk than pies. And if our math checks out, that means they will probably last a little longer too …

Find It: Amazon

#### 14. MARBOTIC SMART NUMBERS; \$39

This hands-on math game makes learning arithmetic engaging and entertaining, and can help kids 3–6 years old recognize units and solve basic additions and subtractions. These wooden letters come with three free apps that you pair with any iPad and most Samsung and Nexus tablets.

Find It: Target

#### 15. HIDDEN FIGURES IN PAPERBACK; \$10

You saw the movie—now delve even deeper into the true stories of Katherine Johnson, Dorothy Vaughan, Mary Jackson, and the other African-American women who worked at NASA as "human computers" during the Space Race. Margot Lee Shetterly's best-seller reveals just how much ground-breaking work these brilliant mathematicians truly did, even while dealing with both gender discrimination and the Jim Crow era. And if you haven't seen the movie, stream it on HBO or purchase it here.

Find It: Amazon

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