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# The Puzzling Collatz Conjecture

The Collatz Conjecture is a relatively simple set of math instructions that lead to a puzzling problem. If you run this set of rules on a given number, and repeat the process, where do you end up? In every case that mathematicians have tried since the problem was first posed in 1937, they've ended up at the number 1, but the experts can't prove that this will be the case for all (positive, whole) numbers. Why not?

Here's the sequence: Pick a number that is a positive integer. (For instance, the number 1 or 100 or 10,123,456.) If it's even, divide it by two. If it's odd, multiply it by three and add one. Take the resulting number and keep running the process.

In this video, professor David Eisenbud runs the number 7 through this process and ends up at 1. At present, mathematicians have run all whole numbers up to 2^60 through this process and they all end up at 1. But the tricky bit is that the path back to 1 is often winding and bizarre, not following an obvious pattern. Why? This is genuinely surprising:

If that's not enough for you, here's another six minutes of footage on the same topic:

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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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See If You Can Solve This Tricky Coin-Flipping Riddle
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Make sure your head is in working order before trying to solve this riddle from TED-Ed, because it's a stumper.

Here's the scenario: You're an explorer who's just stumbled upon a trove of valuable coins in a remote dungeon. Each coin has a gold side and a silver side, each with an identical scorpion seal. The wizard who guards the coins agrees to let you have them, but he won't let you leave the room unless you separate the hoard into two piles with an equal number of coins with the silver side facing up in each. You've just counted the total number of silver-side-up coins—20—when the lights go out. In the dark, you have no way of knowing which half of a coin is silver and which half is gold. How do you divide the pile without looking at it?

As TED-Ed explains, the task is fairly easy to complete, no psychic powers required. All you need to do is remove any 20 coins from the pile at random and flip them over. No matter what combination of coins you choose, you will suddenly have a number of silver-side-up coins that's equal to whatever is left in the pile. If every coin you pulled was originally gold-side-up, flipping them would give you 20 more silver-side-up coins. If you chose 13 gold-side-up coins and seven of the silver-side coins, you'd be left with 13 silver coins in the first pile and 13 silver ones in your new stack after flipping it over.

The solution is simple, but the algebra behind it may take a little more effort to comprehend. For the full explanation and a bonus riddle, check out the video from TED-Ed below.

[h/t TED-Ed]

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