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May 24th, 2022 (Permalink)

What's New?

An article, "How to be a Prophet", is. Since it's a perennial rather than a topical subject, I've placed a link for it under the Main Menu to your left instead of including it here in the Weblog.

Check it out!

New Book
May 6th, 2022 (Permalink)

Puzzle Quest

Quote: "If we see the world as a series of puzzles instead of a series of battles, we will come up with more and better solutions, and we need solutions more than ever."1

Title: The Puzzler

Subtitle: One Man's Quest to Solve the Most Baffling Puzzles Ever, from Crosswords to Jigsaws to the Meaning of Life

Comment: This is a good subtitle if it accurately describes the book but, at the risk of hair-splitting, I'll note that "the meaning of life" is not a "puzzle" in the same sense as a crossword or jigsaw puzzle: it's a philosophical problem. Though philosophical problems are sometimes called "puzzles", unlike crosswords and other recreational puzzles, they're not guaranteed to have solutions. Sometimes the correct answer to a philosophical problem is that there is no solution.

Another demur I have is with the emphasis on solving "the most baffling puzzles ever". As a puzzle solver and occasional creator, I know that it's extremely easy to make puzzles that are extraordinarily difficult, and even unsolvable for all practical purposes. For instance, the puzzle I posted earlier this month involved finding the combination of a lock with only three tumblers2; there are only a thousand possible combinations to such a lock, so it's theoretically possible to solve the puzzle with brute force. However, it would be easy to make such a puzzle harder by simply increasing the number of tumblers: a four-tumbler lock has 10K possible combinations; a five-tumbler one 100K. A puzzle of this type with a lock that had six tumblers, and thus a million possible combinations, would probably be virtually unsolvable.

The trick with puzzle creation is to make one that is difficult enough to be interesting, but not so hard as to cause people to give up in frustration. Most of the fun of puzzles is in successfully solving one, but it's no fun if there's no challenge. Yet, who wants to spend hours or even days trying to solve a puzzle only to fail?

Author: A. J. Jacobs

Comment: I've read Jacobs' previous book The Know-It-All, in which he wrote about his attempt to read all of the Encyclopaedia Britannica, and found it interesting. He reminds me of George Plimpton, who died almost twenty years ago and so is probably not widely known to readers under the age of fifty. Plimpton was a sort of professional amateur who wrote books such as Paper Lion, about playing on a professional football team, and The Bogey Man, in which he played golf against pros. I devoured those books as a kid.

Jacobs appears to be doing something similar in this book: competing in puzzle tournaments against the best solvers and pitting himself against "the most baffling puzzles ever". I haven't read any of Jacobs' other books, because their topics don't really interest me, but The Puzzler really does.

Original Puzzles By: Greg Pliska

Comment: The book includes twenty new puzzles created by Pliska: one for each chapter3. In addition, there's a puzzle contest with a prize of $10K for the winner. To participate in the contest, you have to find a secret passcode that is hidden in the introduction to the book. The introduction can be downloaded free from the book's website4, so you don't have to buy the book to compete in the contest.

Summary: Based on the Table of Contents, the book has chapters on various different types of puzzle: crosswords (Chapter 1), Rubik's cube (2), jigsaws (6), chess problems (12), riddles (13), and so on. I'm not very interested in the Rubik's cube, which I was never able to get anywhere with, and it doesn't take Deep Blue to beat me at chess, so I'm not much interested in those chapters. The most interesting ones to me are chapter 8, on math and logic puzzles, together with chapter 11 on Sudoku and KenKen, which are basically abstract logic puzzles.

Date: 2022

Excerpt: "…[P]uzzles are not a waste of time. Doing puzzles can make us better thinkers, more creative, more incisive, more persistent. I'm not just talking about staving off dementia and keeping our minds sharp. Yes, there's some mild evidence that doing crossword puzzles might help delay cognitive decline…. I'm talking about something more global. It's been my experience that puzzles can shift our worldview. They can nudge us to adopt the puzzle mindset―a mindset of ceaseless curiosity about everything in the world, from politics to science to human relationships―and a desire to find solutions. These insights sparked the idea for the book you are holding now. I decided to embrace my passion and do a deep dive into the puzzle world. I pledged to embed myself with the world's greatest puzzle solvers, creators, and collectors and learn their secrets. I'd try to crack the hardest puzzles in each genre, from jigsaws to crosswords to Sudoku."5

Comment: Based on personal experience, I'm convinced that working puzzles can improve one's problem-solving ability. Solving problems is a skill, and just like other skills such as swimming or piano-playing, it's learned and improved by practice. I'm more doubtful about Jacobs' grandiose notion that puzzles will save the world, though I do think that a problem-solving mindset would help.

Further Reading:

Disclaimer: I haven't finished reading this book yet, so can't review or recommend it. However, its topic interests me, and may also interest Fallacy Files readers.


  1. P. xv, paragraphing suppressed. All page citations are to the new book.
  2. Crack the Combination I, 5/4/2022
  3. P. xvi.
  4. "The Puzzler", accessed: 5/5/2022.
  5. P. xiv.

May 4th, 2022 (Permalink)

Crack the Combination I

The combination of a lock is three digits long, each digit differing from the other two. Here are some incorrect combinations:

  1. 507: One digit is right and is in the right place.
  2. 526: One digit is right but it's in the wrong position.
  3. 785: Two digits are correct but both are in the wrong places.
  4. 908: One digit is right but in the wrong position.

Can you determine the correct combination from the above clues?

May 2nd, 2022 (Permalink)

Hardy or Hearty?

A recent newspaper article on a small town restaurant included the following sentence: "They liked supporting a local business, the hardy yet inexpensive meals and the sense of belonging—even if they’d never been to this particular diner before."1 What the reporter meant was a hearty "yet inexpensive" meal.

"Hardy" means "strong", especially in the sense of surviving difficult circumstances2. "Hardy" applies literally only to living things; for instance, "a hardy plant" is one that would survive a harsh winter. In contrast, "hearty" means "large", or "filling" when applied to food3. So, the breakfast served in the local diner was large despite being cheap.

Obviously, one reason why "hearty" and "hardy" are easy to confuse is that their pronunciations are so similar. In fact, unless enunciated very carefully, they are pronounced identically, at least in American English. Only one of the reference books I routinely check noted that these words are easily confused4, despite the fact that a search of the web shows many examples of such phrases as "hardy meal" and "hardy breakfast", and a book search on Google produces several instances from books and magazines.

Unlike many of the other easily confused pairs of words that we've looked at in this series, the misuse in this case goes both ways. For instance, a web search for "hearty plants" brings up the headline: "Unkillable Plants: Hearty Options for Your Home Office"5, and this from a landscaping site that should know better.

Since both words are English adjectives, it's unlikely that a spelling or grammar checking program will catch the mistake of using one where the other is meant. I checked the sentence from the newspaper article quoted above in my old copy of Microsoft's Word program, as well as three online checkers, and none discovered the mistake. So, file this in your mental checker under "Confusibles".


  1. Salena Zito, "Diner breakfasts are perfectly normal, no matter what D.C. elites think", Pittsburgh Post-Gazette, 3/13/2022.
  2. "Hardy", Cambridge Dictionary, accessed: 5/1/2022.
  3. "Hearty", Cambridge Dictionary, accessed: 5/1/2022.
  4. Bill Walsh, Lapsing Into a Comma: A Curmudgeon's Guide to the Many Things That Can Go Wrong in Print―and How to Avoid Them (2000), p. 144.
  5. "Unkillable Plants: Hearty Options for Your Home Office", Plantscapers, 1/28/2021.

Previous Month

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Recommended Reading
April 30th, 2022 (Permalink)

Against Gatekeeping & "Democracy Dies in Darkness"

April 21st, 2022 (Corrected: 4/30/2022) (Permalink)

Credibility Checking, Part 4: Ballpark Estimation

In the previous installment of this series on how to check claims for credibility1, we needed to know how many teenaged drivers there were in the United States in 2007, which is the sort of very specific statistical fact that you are unlikely to be able to find quickly or at all. Rather than giving up, we estimated the number based on a couple of other facts that we knew or were able to look up quickly: the population of the country and the average life span in that year. Thankfully, in order to check a claim for credibility, we seldom if ever need precise numbers, and ballpark estimates will serve.

What is a "ballpark" estimate? It is an estimate that is "in the ballpark", as we say, that is, it's not spot-on but it's close enough. The use of "ballpark" as a name for this type of estimation appears to have come from rough estimates of the number of spectators in a ballpark watching a baseball game2. We frequently don't need an exact number, which is fortunate since an exact number is often not available. In such situations, we can make do with a ballpark estimate, which I define as one that has the same order of magnitude as the number estimated.

What are orders of magnitude? They are tens, hundreds, thousands, tens of thousands, and so on, but also tenths, hundredths, thousandths, and so forth. For an estimate to be "in the ballpark" means that the estimate and the number estimated both belong to the same order of magnitude.

The best way to learn how to successfully guesstimate numbers is to see examples of how to do so, and then try your own hand at it. You may be surprised at how easy it is―and fun!

An Example

What percentage of the American population dies in automobile accidents?3 This is a statistic that you're unlikely to just happen to know. However, you may well know enough to make a good estimate. If you'd like to try answering this question yourself, stop reading here and do so; then come back and read on to see how I estimated it.

What is it that you need to know to make such an estimate? As discussed in the previous part, a percentage is a type of ratio. To figure the ratio, you need two numbers: a numerator and a denominator. In this case, the numerator is the number of Americans who die in car crashes and the denominator is the total number of Americans who die―since everyone dies, this is simply the total population. Since we're doing a guesstimate, we don't need precise statistics for either of these numbers.

As I've mentioned in previous entries4, the population of the United States is a good landmark number to remember, and it's easy: the current population is approximately a third of a billion. So, that's our denominator.

The numerator is trickier: how many people out of that 330 million population die in traffic accidents? I've also mentioned in previous entries that the number of Americans who die in traffic accidents per year tends to be around 30-40K5; let's use the midpoint, 35K. However, this is not our numerator, since that ratio gives the risk of being killed in a car accident in a year. Luckily, the average American lives to be about 80 years old6, so the numerator we want is 35K × 80, which is approximately three million. Now, the math is so simple that you can do it in your head: three million is about 1/100th of 330 million, so the percentage of Americans who die in automobile crashes is about 1%.

Does the Estimate Hold Up?

Now let's compare our estimate with the one given by Weinstein & Adam in Guesstimation3. They actually formulated the question as: "What fraction of American deaths are caused by automobiles?", but any fraction can be easily turned into a percentage1.

So, for the numerator they used 40K Americans "killed on the roads each year", which they multiplied by 75, life expectancy in 20087, to get three million, which represents the total number of Americans who die in a car crash at some age. That's our numerator.

The denominator for the fraction is 300 million―which was the approximate population of America in 2008 when the book was published8. Again, you can do the math in your head, and the result is the same as our estimate above, which is evidence that it is a good estimate.

Another way to test a ballpark estimate is to compare it to your own experience. If one percent of us die in car accidents, what is the chance that you have known someone who died that way. How many people have you known who have died? Obviously, this depends upon how old you are and how many people you have known. Have you known as many as a hundred people who have died? If so, then you probably knew at least one automotive fatality.

I don't know about you, but I have a hard time remembering all of my relatives, friends, and acquaintances who are gone. Still, it doesn't seem to be close to a hundred, but perhaps around half that many. Nonetheless, one close relative of mine died in a car crash, and a friend of a friend also perished that way. So, if anything, it seems as though our estimate may be on the low side.

Finally, how does our estimate compare to official statistics? The Centers for Disease Control and Prevention (CDC) collect statistics on "leading causes of death", among them "Accidents (unintentional injuries)". According to the most recent data, a total of 3,383,729 Americans died in 20209. However, the CDC does not break out the numbers for accidents involving cars.

Thankfully, another alphabet agency, the National Highway Traffic Safety Administration (NHTSA), collects statistics on automotive deaths. According to an NHTSA press release, 38,680 Americans are estimated to have died in automobile accidents in 202010. This, of course, is close to our midpoint estimate of 35K. Again, you can do the math at a glance: 39K is about 1% of 3.4 million; more precisely, it's 1.1%.

Clearly, by these various measures, our estimate did not just hit the dartboard, it hit the bullseye.


One surprise of this exercise is just how many Americans die in automobiles. Why are we not more alarmed by this fact? Why don't we hear more about driving safety? I suspect that at least part of the reason is that we have grandfathered automotive accidents into our risk assessments. It's almost as if such accidents are simply "acts of God" that we have no control over, so we just accept that one-percent of us will die in a car accident, even though most are preventable.

Finally, this exercise shows that by combining what we know with what we can research quickly―using tools such as Wolfram Alpha―and using only simple math, we can make surprisingly accurate estimates. Such estimates are useful, as we have seen in previous installments, for checking the credibility of claims made by activists, advertisers, and politicians.


  1. Credibility Checking, Part 3: Ratios, Rates & Percentages, 3/27/2022.
  2. Webb Garrison, Why You Say It (1992), p. 175.
  3. This example is based on the second question in section 11.1 of Lawrence Weinstein & John A. Adam's, Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin (2008). This is a useful book for practicing ballpark estimates, though it's heavily skewed toward ones involving physics, perhaps because one of the authors is a physicist.
  4. For instance: A trillion here, a trillion there, and pretty soon you're talking about real money., 9/29/2021.
  5. Credibility Checking, Part 2: Divide & Conquer, 2/4/2022.
  6. "What is life expectancy in the United States?", Wolfram Alpha, accessed: 4/19/2022.
  7. "What was life expectancy in the United States in 2008?", Wolfram Alpha, accessed: 4/20/2022.
  8. "What was the population of the United States in 2008?", Wolfram Alpha, accessed: 4/20/2022.
  9. "Deaths and Mortality", Centers for Disease Control and Prevention, accessed: 4/21/2022.
  10. "2020 Fatality Data Show Increased Traffic Fatalities During Pandemic", National Highway Traffic Safety Administration, 6/3/2021.

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