Author: Chris Higgins

In this riddle from TED-Ed, you’re in a sticky situation. You’re stranded in a rainforest and have accidentally eaten a poisonous mushroom. To survive the poison, you need to lick a very particular frog. But which frog is it?

You can watch the video below for more details, or read this description. The problem is simple: You are poisoned and you know that a particular species of frog produces the antidote, which will cure you if you lick it. But to make things more complex, you know that only female frogs of the species have the antidote—males do not. In this frog species, males and females look identical but males have a distinctive croak. (Males and females also occur in identical proportion in this species.) In one direction, you see a single frog. In another, a group of two frogs sitting together.

From the direction of the two frogs, you hear that distinctive “male frog” croak. Uh-oh! One of those two is definitely male.

As the poison sets in, you have to make a logical decision. You need to find a female frog with the antidote. Are your odds better going toward the group of two (one of which is definitely male), or toward the single unknown frog? And what are those odds, anyway?

Note that in this riddle you are not guaranteed to survive. You’re just trying to take your best shot.

So which to choose, and why?

Watch the video below for a discussion of the problem and how the math stacks up behind one of the choices.

For more resources, consult this TED-Ed page. Once you’ve solved it (or if you’ve given up), you might also be interested in this related math problem.

The compact disc player turns 35 this year. Sony’s first CD player was released on October 1, 1982. At the time of its release, the CD was an enormous step forward in home recording technology—and nerds were excited.

In late 1982, an Australian TV show called Towards 2000 dedicated a lengthy segment to the arrival of the CD, “the ultimate in recorded sound.” In the segment, presenters ran through various significant sound-recording milestones, showing off all sorts of needles, horns, hand-cranks, and so on. The “microgroove” LP was effectively the height of recording technology until 1982.

Nearly three minutes into the TV segment below, we see our first compact disc. Mind blowing! The presenters explain that there is no needle involved—it’s frickin’ lasers.

We get a tour of CD technology, including early players with big clicky buttons. My favorite part of this trip down memory lane comes near the end of the segment, when presenters suggest that one day, CD players might even find their way into cars!

Tune in, and be reminded what mind-blowing tech looked like 35 years ago:

Given a standard 52-card deck, how many possible arrangements of the cards within it are there? Another way to ask this is: If you shuffle a deck of cards, what are the possible number of shuffled permutations?

The answer is, predictably, a whole lot. But the astounding fact is that if you shuffle a deck of cards right now, it’s likely that the order your deck is in has never occurred before in human history.

In fact, the number of deck combinations is so great that if a new deck arrangement were written out every second starting at the Big Bang (which, of course, couldn’t have happened, because cards didn’t exist…but still…), we would still be coming up with new deck arrangements today, and for millions of years in the future. Because playing cards in their current form have “only” existed for centuries, and the possibility space is so enormous, a unique shuffled order is extremely likely.

Check out this TED-Ed video for an explanation of why this is the case, and the specifics of the math involved.

Check out this TED-Ed page for more resources. I particularly enjoyed the bit under “Dig Deeper” discussing the anagram possibilities of the Harry Potter phrase “Tom Marvolo Riddle.”

On February 18, 1930, amateur astronomer Clyde Tombaugh discovered “Planet X” using an astrograph, which is essentially a space camera. Planet X was soon named Pluto, and the rest is a nerd battle of historical proportions.

Tombaugh started as a Kansas farm boy, and did not attend college until after he discovered Pluto. He had a knack for building things, particularly his own telescopes. This got him a job at the Lowell Observatory in Flagstaff, Arizona starting in 1929. He earned the job after mailing in his own hand-drawn observations of the planets Mars and Jupiter, as observed using a hand-made nine-inch reflector telescope.

Tombaugh sought Pluto based on a prediction made by Percival Lowell and William Pickering. They had observed wobble in the outer planets’ orbits, and hypothesized that it was caused by some as-yet-unknown planet in a trans-Neptunian orbit.

On one fateful February day, Tombaugh saw the tiny speck of Pluto on a photographic plate. He found it using a “blink comparator,” a device with which you flip between two images—each taken by the astrograph—and spot tiny dots that move in an unexpected way. It was a tremendous discovery, relying both on high technology and hard work.

Tombaugh went on to college after his discovery (he got a scholarship to the University of Kansas). He continued to work in astronomy for decades, eventually becoming a professor at New Mexico State University. He discovered hundreds of objects (mainly asteroids) in the solar system, and took up writing in his later years.

To remember Tombaugh and his discovery, let’s tune in to this NASA mini-documentary in which his kids, Annette and Alden Tombaugh, remember their father:

For more from the horse’s mouth, here’s an excellent BBC documentary on Tombaugh, which opens with an aging (and quite dapper) Dr. Tombaugh receiving an award. He proceeds to show off his own telescopes and tell his story, including an excellent demo of the blink comparator—using the original Pluto plates!.

(Image of Clyde Tombaugh via Wikimedia Commons, in the public domain.)

Sometimes we need a relaxing background sound. For some, it’s the Star Trek ship sound. For others, sleep-inducing podcasts are the way to go. For Netflix fans, there’s an oscillating fan.

Today, I am proud to present 10 hours of ambient sound, featuring a polar icebreaker in a storm. The sound is part live recording, part synthesized audio, and the video features a static shot of a Norwegian research vessel. The net effect is truly relaxing, conducive to background sound for reading, sleeping, bathing, you name it. From the YouTube description:

10 hours video of Arctic ambience with frozen ocean, ice cracking, snow falling, icebreaker idling and distant howling wind sound. Natural white noise sounds generated by the wind and snow falling, combined with deep low frequencies with delta waves from the powerful icebreaker idling engines, recorded at 96 kHz – 24 bit and designed for relaxation, meditation, study and sleep.

Crank this up and relax:

Relevant reading: Why Is White Noise ‘White’?

[h/t: Boing Boing.]

Mathematician Søren Eilers was intrigued by a LEGO-related math problem. Let’s say you have six “standard LEGO bricks” (the rectangular 4×2 bricks seen in the original LEGO patent). If you fit them together, how many possible structures can you make?

This question was first officially “answered” in 1974, and LEGO mathematicians arrived at the number 102,981,500. Eilers was curious about the mathematical methodology behind that number, and soon discovered that it only covered one kind of stacking—thus, it was dramatically low. So he wrote a computer program that modeled all the possible brick combinations. After running the program for a week, he ended up with a massive number: 915,103,765 combinations.

(Incidentally, Eilers encouraged high school student Mikkel Abrahamsen to write another program in a different programming language, on a different computing platform, without consulting on the solution or methodology. When Abrahamsen’s program concluded, the math matched up—and Abrahamsen’s method for computing it was actually superior!)

Then, of course, Eilers had to ask what happened if you added a seventh brick, or an eighth, and so on. The math gets exponentially more time-consuming with each addition. Even with a revised version of his program running on a modern computer (which can now handle the original six-block calculation in just five minutes), calculating the eight-brick solution takes about three weeks, and a nine- or ten-brick solution would “probably take years. Maybe hundreds of years.”

Here’s a brief clip from the documentary A LEGO Brickumentary in which Eilers explains how it all came together:

Of course, because Eilers is a math professor, he put all the math online for fellow nerds to peruse. There’s a lot on that page to digest. I enjoyed this snippet from the page in which he considers the possibility of a 25-brick solution (emphasis added):

With the current efficiency of our computer programs we further estimate that it would take us something like

130,881,177,000,000,000,000,000,000,000,000,000,000,000

years to compute the correct number. After some 5,000,000,000 years we will have to move our computer out of the Solar system, as the Sun is expected to become a red giant at about that time.

If you like this stuff (and have the math skills to decipher it), dig into the academic paper “On the entropy of LEGO” by Bergfinnur Durhuus and Søren Eilers.

Here’s a nice riddle. Three members of a team have been captured. On their way into the prison (guarded by ravenous mutant salamanders), they pass a series of numbered doorways, each with a keypad featuring the numbers one through nine. Each keypad opens with a code…but you have no idea what that code might be. One member will be allowed to try to escape by facing a challenge. Can the remaining two listen in on that challenge, figure out the correct hallway, and figure out the passcode to open it? With some basic math, they can succeed.

Some more details: Zara, the team member participating in the challenge, has a one-way audio transmitter that allows the other two team members to listen. As Zara is led to the challenge through one of the hallways, she is informed that her challenge is to guess the passcode for her hallway based on rules. Zara is told that the passcode will contain three positive whole numbers, in ascending order (like 1, 2, 3—the second number is greater than or equal to the first, the third likewise to the second).

Zara is told that she may ask up for up to three clues about the code—but she can’t say anything else, or else she too will be fed to the mutant salamanders! Through this process of requesting clues and thinking through the problem, Zara implicitly passes information to her compatriots about what the answer is.

Zara asks for the first clue, and is told that the product of the three numbers in the code (x * y * z) is 36. Zara asks for the second clue, and is told that the sum of the numbers in the code (x + y + z) is the same as the number of the hallway she entered. There is a long silence. Then she asks for the third clue, and is told that the largest (greatest) number appears only once in the combination. Shortly after, Zara punches in the code and escapes.

Given that information, can you figure out the passcode? The video below walks through the puzzle and its solution. Here’s the text of the puzzle in its simplest form, transcribed from the video (it helpfully asks you to pause before explaining the solution!):

Find three numbers in ascending order!

1. The product of the three numbers is 36.

2. The sum of the three numbers is the same as Zara’s hallway number, which you don’t know but she does.

3. The largest number must be unique.

4. Zara, a perfect logician, needed clues 1-3 to escape.

Start your figuring!

Then tune in to the video to test your solution:

For a bit more on this puzzle, check out this TED-Ed page, especially the “Dig Deeper” section which contains links to various math resources that you may find useful. (It also includes a link to a puzzle variant that may be interesting after you solve this one.)

On February 10, 1942, Glenn Miller was awarded the first-ever Gold Record, for the song “Chattanooga Choo Choo.” RCA Victor made the record by taking one of Miller’s albums, painting it gold, and framing it. The event celebrated 1,200,000 sales of the single, released on RCA Victor’s Bluebird label in 1941.

“Chattanooga Choo Choo” was a massive hit, and in 1942 Miller was at the height of his career, performing with his orchestra to sold-out houses. It was also the height of World War II. Miller was 38—too old to be drafted—but he volunteered for the Army and was quickly promoted to captain, then major. (Incidentally, he tried the Navy first, but they turned him down.)

Miller’s job in the Army was primarily to provide music to the troops, mainly within the Air Force. In addition to performing, he modernized the Army Band tradition and rewrote a variety of key tunes. After hundreds of performances in the U.S. and abroad, Miller’s single-engine plane was lost in 1944 on a flight from England to Paris. He was 40 years old.

But let’s get back to the good stuff—”Chattanooga Choo Choo” appeared in the 1941 film Sun Valley Serenade, and that performance is a barn-burner. Lasting eight minutes, the “Choo Choo” segment starts with the Glenn Miller Orchestra rehearsing the tune, featuring whistling and singing by Tex Beneke, Paula Kelly, and The Modernaires.

Just when you think the song is over, the camera pans to reveal a second, previously unseen set—a train station where Dorothy Dandridge and The Nicholas Brothers appear and perform an exquisite song-and-dance number, while the orchestra continues.

Come for the swing, stay for the tap. (If you just want to see the fantastic dance bit featuring The Nicholas Brothers, I won’t blame you—zip ahead to 4:55.)

For a bit more on Miller and his gold record-winning song, read this Rhapsody in Books blog post. If you’ve never seen The Nicholas Brothers before, watch them perform “the greatest dance number ever filmed.”

(Glenn Miller image, public domain, courtesy of Wikimedia Commons.)

Julia Child started her public TV show The French Chef on February 11, 1963. In her first black-and-white episode, she made Boeuf Bourguignon, spending a half hour in the kitchen, recording the show live. Child’s show came to define the TV cooking show genre, though many of us have never actually seen her original series. (Though you may have seen her kitchen at the Smithsonian’s National Museum of American History!)

Here’s Child’s first episode, part of a massive playlist of her early work:

One nerdy note about this first episode is that it was recorded on kinescope. This process meant that live TV cameras were pointed at Child, switched live (cutting in to closeups of her hands and such), all while a film camera was pointed at a TV monitor in order to record the program. That film was later used for broadcast. In the very first episode, the lighting is a bit dim, sometimes making it hard to see details. As those early episodes proceed, you can watch the production crew adding lighting, overhead cameras, and eventually recording the show to tape.

For more on Child, enjoy: 15 Delicious Facts About Julia Child; What Julia Child’s Thanksgiving Was Like; and Julia Child’s Recipe for Shark Repellent.