A Logic Puzzle That Teaches a Life Lesson

Here are a couple classic logic problems, updated for the digital world.

A Logic Puzzle That Teaches a Life Lesson


Before we get to the brain teaser of the day — which does, as the headline indicates, carry a deeper meaning — here is a classic logic problem, updated for the digital world, to get you warmed up: 

Puzzle #1

You find yourself in a dark chamber with two closed doors — one leading to bliss, the other to death, though you do not know which door is which. Two charged and ready iPhones — one programmed with Honest Omniscient Siri, the other with Lying Omniscient Siri — sit on a low table. (Honest Siri always tells the truth; Lying Siri always lies.) But the phones appear identical, and, again, you have no idea which is which. You must choose a door, and you are given permission to ask one of the phones a single question to help you make your decision. What question do you ask?

Tough one, right? Sweating a little? It would be easy as pie if you could ask two questions: one to establish which is Honest Siri (e.g., “What’s my name?”) and then one directed to Honest Siri to determine which door leads to bliss. But no such luck. You need to ask a single question with no idea which phone is the trustworthy one. Make it a good one.

Solution:

Because your question needs to yield valuable information no matter whether you happen to address Honest Siri or Lying Siri, it should be a question that will give you the same answer no matter which phone you chanced to pick up. So here we go: “If I asked the other iPhone which door leads to bliss, what would Siri tell me?” Honest Siri will point toward the death door, which is what Lying Siri would in fact indicate. Lying Siri would point toward the death door as well, which is the opposite of what Honest Siri would tell you if you asked her directly. So you find out what you need to know about the doors without having to figure out which phone is which. Now that you know which is the door to your demise, you can open the other door with confidence that bliss awaits you on the other side.

In this problem, known as the two guards riddle, everything depends on several pieces of information you assume to be true: The doors really lead to divergent fates and one phone always lies while the other always tells the truth. But in the real world, such conditions are always subject to some degree of doubt.

Puzzle #2

A new puzzle from programmer Mark Dominus plays on this inevitable uncertainty, and contains a valuable lesson. He calls it the “annoying boxes problem.” Here it is:

There are two boxes on a table, one red and one green. One contains a treasure. The red box is labeled "exactly one of the labels is true." The green box is labeled "the treasure is in this box."

Can you figure out which box contains the treasure?

a. The treasure is in the red box

b. The treasure is in the green box

c. There is not enough information to determine the answer

d. Something else: __________________________

Pencils down.

What was your answer? Before I share the correct solution and an explanation thereof, here is the rundown of how 506 people voted in early July when Dominus first posted the puzzle:

Solution

So if you said the treasure is in the red box, you are in good company: About two-thirds of respondents chose (a), by far the most popular response. But if you selected option (c) — not enough information — you arrived at the correct answer. But here’s the kicker: The treasure was in the green box. How could that be? Here is how Dominus explains the apparent contradiction:

If you said the treasure was in the green box, you were right, but you got the logic puzzle wrong. As Dominus points out, the question asks whether you can figure out which box the treasure is in. And the answer to that question is no. No points for lucky guesses.

If you selected (a), like most respondents, you might wonder why you’re wrong. Dominus goes into detail in his post, which you can read here. For me, the most interesting point Dominus makes comes in his explanation of why it’s a mistake to read too much (or to read anything, actually) into the labels on the boxes. They are “red herrings,” he writes, and are “worthless”:

[I]n the absence of additional information, there is no reason to believe that the labels give any information about the contents of the boxes, or about labels, or about anything at all. This should not come as a surprise to anyone. It is true not just in annoying puzzles, but in the world in general. A box labeled “fresh figs” might contain fresh figs, or spoiled figs, or angry hornets, or nothing at all.

The boxes puzzle is “annoying” because it unsettles our predilection to place faith in truth claims and use them as anchors when solving a puzzle—or navigating the world. But jogging our tendency to rely on labels is a valuable public service. Labels can mislead; they can confuse; they can be crafted to manipulate you to do something you wouldn’t otherwise do. Have you ever clicked on a link with an especially alluring headline that didn’t quite deliver? Selected a product labeled “all natural” at the grocery store without knowing whether it was really any healthier? Bought a sunscreen based on its stated sun-protection factor (SPF) with no idea what that really means?

We have no choice, but to rely on labels, of course. Radical skepticism about every label is a prescription for paralysis. But it’s still advisable to keep up our guard in the face of labels that seem outlandish, unlikely, inconsistent, or too good to be true — and Dominus’ annoying little logic puzzle is a nice reminder of that.

Image credit: Shutterstock

Follow Steven Mazie on Twitter: @stevenmazie

Massive 'Darth Vader' isopod found lurking in the Indian Ocean

The father of all giant sea bugs was recently discovered off the coast of Java.

A close up of Bathynomus raksasa

SJADE 2018
Surprising Science
  • A new species of isopod with a resemblance to a certain Sith lord was just discovered.
  • It is the first known giant isopod from the Indian Ocean.
  • The finding extends the list of giant isopods even further.
Keep reading Show less

Volcanoes to power bitcoin mining in El Salvador

The first nation to make bitcoin legal tender will use geothermal energy to mine it.

Credit: Aaron Thomas via Unsplash
Technology & Innovation

This article was originally published on our sister site, Freethink.

In June 2021, El Salvador became the first nation in the world to make bitcoin legal tender. Soon after, President Nayib Bukele instructed a state-owned power company to provide bitcoin mining facilities with cheap, clean energy — harnessed from the country's volcanoes.

The challenge: Bitcoin is a cryptocurrency, a digital form of money and a payment system. Crypto has several advantages over physical dollars and cents — it's incredibly difficult to counterfeit, and transactions are more secure — but it also has a major downside.

Crypto transactions are recorded and new coins are added into circulation through a process called mining.

Crypto mining involves computers solving incredibly difficult mathematical puzzles. It is also incredibly energy-intensive — Cambridge University researchers estimate that bitcoin mining alone consumes more electricity every year than Argentina.

Most of that electricity is generated by carbon-emitting fossil fuels. As it stands, bitcoin mining produces an estimated 36.95 megatons of CO2 annually.

A world first: On June 9, El Salvador became the first nation to make bitcoin legal tender, meaning businesses have to accept it as payment and citizens can use it to pay taxes.

Less than a day later, Bukele tweeted that he'd instructed a state-owned geothermal electric company to put together a plan to provide bitcoin mining facilities with "very cheap, 100% clean, 100% renewable, 0 emissions energy."

Geothermal electricity is produced by capturing heat from the Earth itself. In El Salvador, that heat comes from volcanoes, and an estimated two-thirds of their energy potential is currently untapped.

Why it matters: El Salvador's decision to make bitcoin legal tender could be a win for both the crypto and the nation itself.

"(W)hat it does for bitcoin is further legitimizes its status as a potential reserve asset for sovereign and super sovereign entities," Greg King, CEO of crypto asset management firm Osprey Funds, told CBS News of the legislation.

Meanwhile, El Salvador is one of the poorest nations in North America, and bitcoin miners — the people who own and operate the computers doing the mining — receive bitcoins as a reward for their efforts.

"This is going to evolve fast!"
NAYIB BUKELE

If El Salvador begins operating bitcoin mining facilities powered by clean, cheap geothermal energy, it could become a global hub for mining — and receive a much-needed economic boost in the process.

The next steps: It remains to be seen whether Salvadorans will fully embrace bitcoin — which is notoriously volatile — or continue business-as-usual with the nation's other legal tender, the U.S. dollar.

Only time will tell if Bukele's plan for volcano-powered bitcoin mining facilities comes to fruition, too — but based on the speed of things so far, we won't have to wait long to find out.

Less than three hours after tweeting about the idea, Bukele followed up with another tweet claiming that the nation's geothermal energy company had already dug a new well and was designing a "mining hub" around it.

"This is going to evolve fast!" the president promised.

How Pfizer and BioNTech made history with their vaccine

How were mRNA vaccines developed? Pfizer's Dr Bill Gruber explains the science behind this record-breaking achievement and how it was developed without compromising safety.

How Pfizer and BioNTech made history with their vaccine
Sponsored by Pfizer
  • Wondering how Pfizer and partner BioNTech developed a COVID-19 vaccine in record time without compromising safety? Dr Bill Gruber, SVP of Pfizer Vaccine Clinical Research and Development, explains the process from start to finish.
  • "I told my team, at first we were inspired by hope and now we're inspired by reality," Dr Gruber said. "If you bring critical science together, talented team members together, government, academia, industry, public health officials—you can achieve what was previously the unachievable."
  • The Pfizer-BioNTech COVID-19 Vaccine has not been approved or licensed by the Food and Drug Administration (FDA), but has been authorized for emergency use by FDA under an Emergency Use Authorization (EUA) to prevent COVID-19 for use in individuals 12 years of age and older. The emergency use of this product is only authorized for the duration of the emergency declaration unless ended sooner. See Fact Sheet: cvdvaccine-us.com/recipients.

Keep reading Show less
Quantcast