October 2nd, 2022 (Permalink)
Shear or Sheer?
A book I just read includes the following sentence: "In recent years, the greatest growth in the shear quantity of statistical indicators has been in the field of education.1" "To shear" is a verb that means cutting the wool from a sheep or, more generally, cutting hair close to the skin, or close cutting of some sort2. However, it's an adjective rather than a verb in the above sentence. As a noun, it has a technical meaning in geology, and it can be used as an adjective, as in, "shear force" and "shear strength", but not, as far as I know, "shear quantity". Anyway, this meaning wouldn't make sense in the above sentence: how would a technical geological term apply to educational statistics?
In contrast, "sheer" is an adjective with a wide range of meanings depending on the noun it modifies: "complete", "unqualified", "thorough", or "utter", as in "sheer nonsense" or "sheer luck"; "steep", as in "sheer slope"; or "thin", as in "sheer fabric"3. It's hard to see what connects these different meanings, but it seems to be extremity; for instance, a sheer slope is extremely slanted, a sheer fabric is as thin as you can get, and sheer nonsense is thoroughly nonsensical. A type of extremity is purity or lack of dilution, so that sheer foolishness is pure foolishness undiluted by even a drop of sense.
However, some uses of "sheer" seem to serve simply as emphasis, that is, as a way of underlining a word or putting it in italics. The author of the book seems to have used "sheer" in this way, so that we could paraphrase the sentence: "The greatest growth in the quantity of statistical indicators has been in the field of education."
Since both are proper English words, a sheer spell-checking program will not shear the mistake from your prose. However, given that one of the two spellings is usually a verb, while the other is an adjective, a program that checks grammar may mark the error. My old copy of Microsoft Word, when given the example sentence, flagged the word "shear" as a "Possible Word Choice Error", and suggested "sheer" as a correction. Well done! In comparison, out of several free online spell-checking programs I checked, only one caught it.
In sum, if you habitually use a spell-checking program, you might want to check it to see if it will catch this error. Either that, or file it away in that spell-checker in your head called a "brain".
- Gary M. Klass, Just Plain Data Analysis: Finding, Presenting, and Interpreting Social Science Data (2008), p. xvii.
- "Shear", Cambridge Dictionary, accessed: 10/1/2022.
- "Sheer", Cambridge Dictionary, accessed: 10/1/2022.
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September 30th, 2022 (Permalink)
Junk Journalism & Facts Come Last
Thou shalt not raise a false report: put not thine hand with the wicked to be an unrighteous witness.1
- Jesse Singal, "How the Media Fell for A Racism Sham", Common Sense, 9/15/2022
Last month, Rachel Richardson―the only black starter on the women’s volleyball team at Duke University―leveled a shocking accusation. She said that during her team’s August 26 match against Brigham Young University, fans inside the BYU arena in Provo, Utah inundated her with racist abuse and threats. … For its part, BYU quickly acknowledged that something horrible had happened in the fieldhouse. The day after the game, it published an apologetic statement, saying that the fan deemed responsible for shouting the epithets―who was not a BYU student―had been banned from all university athletic venues. …
For millions of people watching this story unfold, this was yet another example of the ineradicable stain of American racism, of just how little progress we’ve really made. Except it didn’t happen. There is no evidence that the chain of events described by Richardson and her family members occurred. There isn’t even evidence a single slur was hurled at her and her teammates, let alone a terrifying onslaught of them.
All the journalists who credulously reported on this event were wrong―and it was an embarrassing kind of wrong, because the red flags were large, numerous, and flapping loudly. Richardson and her family members reported that racial slurs had been hurled with abandon, loudly and repeatedly, in a crowded gym filled with more than 5,000 people. But the journalists covering this incident never stopped to notice how odd it was that none of these vile slurs were captured by any of the thousands of little handheld cameras in the gym at the time, nor on the bigger cameras recording the match2. Nor did they find it strange that in the days following the incident, not a single other eyewitness came forward―none of Richardson’s black teammates, and none of the players for either team.
Instead of heeding the red flags and slowing down to ask some questions, mainstream journalists simply consumed and regurgitated the story as it had been fed to them…. If any of these journalists had demonstrated an iota of curiosity or skepticism―if they’d practiced journalism as it was meant to be practiced―they could have had a major scoop. Instead they acted as stenographers, with terrible results. …
I call this "junk journalism" because, like junk food, it's fast, cheap, and bad for you.
BYU issued another statement that completely imploded the dominant storyline about this incident. The university explained that it had conducted a thorough investigation of the evening’s game, including extensive review of the available video footage and interviews with more than 50 individuals in attendance, and had not found evidence of a single fan yelling a single slur. The ban on the innocent fan had been lifted. …
From the outright criminal fraud of Jussie Smollett―in which some of the most prominent journalists in the world accepted a storyline that never really made much sense―to the unwarranted piling on of the Covington Catholic High School kids, there’s an established pattern of journalists being far too credulous when these incidents first burst onto the scene.
There are real-world consequences to this sort of shoddy reporting, not just for newspapers’ reputations and their pocketbooks…, but for those caught in the crossfire. In this case, a vulnerable, innocent young man was wrongly accused of horrendous acts, and an entire student body was slandered. Millions of people will continue to believe this incident occurred, because debunkings never travel a tenth as far and wide as misinformation does.
It won’t take some radical revolution for journalists to better cover fast-developing, controversial incidents involving race and other hot-button issues. All they have to do is rediscover norms that are already there, embedded in journalistic tradition. … They can adhere to these norms without becoming a shill for the powerful. It’s simply a matter of approaching a story with curiosity and skepticism, of not believing they are the advocate for one side in a conflict―no matter how righteous and obvious the battle lines may seem at first glance.
One norm violated in all of these cases is "innocent until proven guilty". This is not a specifically journalistic norm; instead, it's a legal one, but it's also a more general, ethical norm. One should not believe unproven allegations against people, nor repeat them as if they are true. To do so is to slander those accused if the allegation turns out to be false. Reporters, of course, should report such allegations, but not as if they are facts.
There is at least some reason for hope:
- Zachary Leeman, "CNN’s John Avlon Acknowledges Widespread Media Failure on BYU Racist Heckling Allegations: ‘There Was a Rush to Judgment’", Mediaite, 9/12/2022
CNN’s John Avlon provided some “journalistic accountability” for his network and others during a new segment Monday he dubbed “Upon Further Review.” Avlon tackled the findings from an investigation by Brigham Young University that found no evidence to back up allegations from Duke University volleyball player Rachel Richardson that she and other athletes were subjected to racist heckling.
In a statement about the alleged incident, BYU said they’d interviewed dozens of people, reviewed video and audio evidence, and found nothing to back up the claim that fans were hurling racist slurs at players. … The CNN anchor noted the story jumped to the front of the “outrage Olympics” and his new segment was to update the “initial official version of the story once more facts come in.” He added at one point that CNN was one of many networks to jump on the initial allegations, even inviting Richardson’s family on-air.
“Healthy skepticism is always a virtue, but this doesn’t read like a coverup. Instead, it feels like there was a rush to judgment because of a well-intentioned impulse to believe the Duke player’s accusations,” he said. …
"Well-intentioned"? It may be well-intentioned towards the sole accuser, but not towards those falsely accused of "hurling racist slurs at players".
Facts, however, “always have to come first,” he added. Avlon called for the media to report on the new facts in the Duke University scandal with the same “intensity” they reported on the initial allegations. “Fidelity to the facts is all that we as journalists and citizens should ask,” Avlon said. “It’s understandable that there’s a desire to believe people when they say they’ve been victimized, but the accusations have to be backed up by facts and when the facts don’t fit upon further review, we need to set the record straight with as much intensity as the initial reports.”
Facts should come first, but they usually come last. Initial reports of incidents such as this are often incorrect, so they should be treated as unproven allegations. Later reports may correct the original false ones, but such corrections usually are seen by a fraction of those who saw the original false claims. The organizations that spread such false accounts are, perhaps understandably, reluctant to give as much attention to the truth as they did to the false account, since the truth makes them look bad. As a result, the general effect of junk journalism is to misinform people.
I wish Avlon good luck in his efforts to bring accountability to his network; he'll need it.
- Exodus 23:1-2 (KJV).
- You can watch the match here: "Duke vs BYU Aug. 26, 2022 NCAA", YouTube, 8/27/2022.
Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole. In abridging them, I have sometimes changed the paragraphing and rearranged the order of the excerpts in order to emphasize points.
September 22nd, 2022 (Permalink)
Is the pandemic over?
Last Sunday, in an interview broadcast on the television show 60 Minutes, the President of the United States was asked: "Is the pandemic over?" He answered:
The pandemic is over. We still have a problem with COVID. We're still doing a lot of work on it. But the pandemic is over. If you notice, no one's wearing masks. Everybody seems to be in pretty good shape. And so I think it's changing. And I think this is a perfect example of it.1
In the days since, this has been declared a "gaffe"2. Biden is, of course, notorious for gaffes. A "gaffe" is not necessarily a lie, though some lies are gaffes. Ten years ago, Dan Amira produced a taxonomy of political gaffes3, including the Glaring Factual Error Gaffe, the Hot Mike Gaffe, and the Kinsley Gaffe. Unlike the Hot Mike Gaffe, the Kinsley Gaffe is named for pundit Michael Kinsley, who first identified it. As Amira explains: "…[A] Kinsley gaffe is defined as when a politician accidentally tells the truth." Biden is responsible for gaffes of every type in Amira's taxonomy, but "the pandemic is over" appears to be either a glaring factual error or a Kinsley one.
Way back in April, Anthony Fauci stated three times in an interview that we were out of the pandemic phase of the disease4. That this was also a gaffe was apparent from the fact that he almost immediately tried to take back what he had said. Since Sunday, the White House has tried to do to Biden what Fauci did to himself, but Biden's claim was so clear and straight-forward that it's difficult to spin5.
In addition to the White House undercutting Biden's claim, the major news media began trying to undermine it. For instance, The New York Times published an article under the following headline:
Biden Says the Pandemic Is Over.
But at Least 400 People Are Dying Daily.6
Taken out of context, numbers such as this are almost meaningless. Is 400 a big number or a small number? Compared to what? To give it some perspective, let's compare it to some other diseases. Almost 2,000 people died per day of heart disease in 2020, the most recent year for which data is available7, and over 1,600 died of cancer each day of the same year8. Are heart disease or cancer pandemics? If not, why not?
This raises the question: what exactly is a pandemic? I briefly discussed this question back in early 2020 when the epidemic first began9. According to my dictionary of epidemiology, a "pandemic" is "[a]n epidemic occurring worldwide or over a very wide area, crossing international boundaries, and usually affecting a large number of people10". A textbook that I happen to have has a similar definition: "Pandemic…is an epidemic that is widespread across a country, continent, or a large populace, possibly worldwide.11" These definitions are almost hopelessly vague: How wide is a "wide area"? How large is a "large populace"?
The only definition I was able to find on the Centers for Disease Control and Prevention (CDC) website defines "pandemic" simply as "[a] worldwide epidemic"12, and "epidemic" as "the occurrence of disease within a specific geographical area or population that is in excess of what is normally expected.13" But what is normally expected for a disease that's only been around for a couple of years?
The World Health Organization (WHO) used to have a page that said: "[a] pandemic is the worldwide spread of a new disease.14" This adds the new factor of novelty to the dictionary definition. So, according to this definition, one reason why heart disease and cancer are not considered pandemics is that they are not new. But COVID is now over two years old; is that still "new"?
So, who decides when a pandemic ends, if not the president? Not the WHO. While the WHO's declaration in 2020 that COVID was a pandemic may have contributed to the subsequent panic in the U. S.9, it has now publicly disavowed "officially" declaring an end to it15.
So, is the pandemic over? Don't ask me! The definitions that I've been able to find have been so vague that there doesn't appear to be a clear answer to the question. Apparently, even the president can't get away with declaring it over, so I'm not going to try.
- Scott Pelley, "President Joe Biden: The 2022 60 Minutes Interview", CBS News, 9/18/2022.
- Cecelia Smith-Schoenwalder, "White House Defends Biden’s ‘Pandemic is Over’ Comment Despite Criticisms", U. S. News & World Report, 9/20/2022.
- Dan Amira, "A Taxonomy of Gaffes", New York Magazine, 6/14/2012.
- See: Don't Get Fooled Again & Sweeping it Under the Rug, 5/31/2022.
- Betsy Klein, "White House says Covid-19 policy unchanged despite Biden's comments that the 'pandemic is over'", CNN, 9/19/2022.
- Sheryl Gay Stolberg, "Biden Says the Pandemic Is Over. But at Least 400 People Are Dying Daily.", The New York Times, 9/19/2022. The CDC's weeklong moving average is 356 deaths a day as of two days ago; see: "Trends in Number of COVID-19 Cases and Deaths in the US Reported to CDC, by State/Territory"
September 15th, 2022 (Permalink)
Who's Counting? John Allen Paulos!
Quote: "Too many of us are…innumerate, and this societal innumeracy remains a vastly underrated driver of bad policy and bad politics. Almost every major issue and many minor ones facing this country are made more difficult by believing that (or at least acting as if) the numbers, probabilities, and relative magnitudes relevant to them don't really matter. Unfortunately, the problem involves not only the formal properties of these figures but also an understanding of what they mean or, more frequently, don't mean and how they should be interpreted."1
Title: Who's Counting?
Comment: This month's new book is hot off the presses having just been released today. The title is the same as that of the author's former column for ABC News; I've previously mentioned or discussed here a few of those columns. The book itself is, I gather, a collection of the columns together with some other articles and additional commentary.
Subtitle: Uniting Numbers and Narratives with Stories from Pop Culture, Puzzles, Politics, and More
Comment: Speaking of puzzles, this is a rather puzzling subtitle: "narratives" and "stories" are basically the same thing―aren't they?―in which case the book unites numbers and stories with stories. There must be a better way of saying whatever this subtitle is trying to say. I guess that whoever wrote this―probably not the author but somebody who works for the publisher―wanted to get "stories" and "pop culture" in there so that the innumerate would not be scared away. I doubt that works.
Author: John Allen Paulos
Comment: I've mentioned Paulos frequently on this weblog over the years, and I've read several of his previous books. I particularly like his earlier book A Mathematician Reads the Newspaper, which I shamelessly imitated for the previous entry.
Summary: Paulos summarizes the book as follows:
The book may be considered a mathematical sampler. … Some of the columns will be relevant to public policy questions and will involve misconceptions that are unfortunately perennial. Another group, perhaps more fun, will deal with puzzles and paradoxes since an appreciation of recreational mathematics and a feel for its sometimes counterintuitive conclusions is likely to make one more sensitive to the beauty and even the utility of mathematics. Still another group will offer a conception of mathematics broader than that of a discipline devoted solely to calculation and theorem-proving. I include commentaries on the columns, some quite extended, as well as a good number of more recently written pieces….
The broad topics discussed are puzzles, a bit of probability, lies and logic, (mis)calculations, political partisanship, and religious dogmatism. Among the specific topics discussed are the following: What does Lanchester's law have to do with guerrilla warfare? How can two losing strategies be combined into a winning strategy? What is the relation between "sexonomics" and prostitution? How can Kruskal's card paradox be used to dupe the gullible and explain "happiness"? Did a 13th-century German monk discover the Mandelbrot set long before Benoit Mandelbrot did? Is denying a bit of disinformation always a good strategy? What does Wolf's dilemma reveal about political parties' unity? What is complexity, and how can it illuminate an intuition behind Godel's famous incompleteness theorem? Should we require that presidential candidates solve some very basic math problems, and of what sort? How is it that the number e, 2.718281…, pops up in so many common situations? What is the relationship between the quantitative and the narrative aspects of a story? Should Joe DiMaggio's hitting streak have an asterisk attached? How can the right metaphors increase our understanding of mathematical notions? What is a fundamental flaw in probability that vitiates creationist arguments? What do coincidences, apophenia, and coin flips say about eyewitness testimony, blood clots, and any number of other issues?2
The Blurbs: As you might expect, the book is favorably blurbed by several Big Names, including Neil deGrasse Tyson, Keith Devlin, and Philip Tetlock.
Disclaimer: This is a new book and I haven't read it yet, so can't review or recommend it. However, its topic interests me, and may also interest Fallacy Files readers.
September 9th, 2022 (Permalink)
No one pretends that democracy is perfect or all-wise. Indeed it has been said that democracy is the worst form of government except all those other forms that have been tried from time to time.1
Earlier this month, former Alaska governor and candidate for Vice President, Sarah Palin, lost a special election held to fill the congressional seat for Alaska that was vacant due to the incumbent's death2. The election used an unusual voting system called "ranked-choice" voting, and some of Palin's fellow Republicans blamed her loss on the new system3. What is this system of voting, and did it cost Palin the election?
Most elections in the United States are by plurality voting4, which means that voters vote for only a single candidate for each office and the one who gets the most votes wins the election. Since the plurality system is ubiquitous here, we tend to think that it's the only way to vote, but it's only one among several possibilities.
One disadvantage of the plurality system is that, unless there are only two candidates for a seat, there is no guarantee that the winner will receive a majority of votes, that is, more than 50%. If there are three candidates, it's possible to win an election with as little as 34% of the votes, which means that almost two-thirds of voters preferred a different candidate. For instance, when Abraham Lincoln was elected to his first term, he ran against three other candidates, and received slightly less than 40% of the popular vote5. In other words, Lincoln was elected by a "plurality", that is, less than a majority but more votes than any other candidate received. In America, we say that the majority rules, but it's often a minority that elects.
That a candidate may win with less than a majority of votes is, in fact, the main criticism of the plurality system of voting, especially when the result is due to "vote splitting"6. Suppose there is an election in which three candidates are running: a moderate liberal, an extreme liberal, and a conservative. Suppose, further, that the election takes place in a state where the majority of voters are liberal. In a plurality system, the liberal vote may be split between the moderate and the extreme candidate, and the conservative may win with a plurality of votes. In this way, a conservative could win in a liberal state, or vice versa.
This is not just a logical possibility, but something that has happened repeatedly in American history7; for instance, in the presidential election of 19928, in addition to the usual Republican and Democratic candidates, there was an unusually popular independent, namely, Ross Perot. Perot received nearly 19% of the popular vote, and the Democrat, Bill Clinton, was elected with only a plurality of 43%. It's widely thought, though impossible to prove, that the conservative vote was split between the incumbent Republican, George H. W. Bush, and the more moderate Perot, and that Clinton would not have won otherwise.
Other systems of voting have been devised in an attempt to prevent "spoiler"9 candidates from splitting the vote and creating plurality wins. One of these is "ranked-choice" voting―also known as "alternative vote" (AV)10. In an AV election, voters rank the candidates from favorite to least favorite and, if no single candidate is favored by the majority―which can happen only if there are more than two candidates―the one who received the fewest first-place votes is eliminated. The eliminated candidate's votes are redistributed to the remaining candidates based on second-place votes, and this process continues until one receives a majority of votes11, which is why it's sometimes called an "instant-runoff" election12.
There were three candidates in the special election in Alaska: Republican Palin, Republican Nick Begich, and Democrat Mary Peltola, the eventual winner. The first round vote count was: Peltola, 40%; Palin, 31%; and Begich, 28.5%, so no individual candidate had a majority13. As a result, in the second round, the third-place finisher, Begich, was eliminated and his votes redistributed to Peltola and Palin based on second choices. The final result was: Peltola, 51.5% and Palin, 48.5%.
Alaska is the largest U. S. state by area, but it has a comparatively small population and, as a result, only one seat in the House of Representatives. It's also a conservative state, having gone for Donald Trump in the last presidential election by ten percentage points14, yet the Democrat managed to win its only House seat.
Another argument for the AV system is that it avoids the frequent result in a plurality vote in which a candidate wins with less than a majority. However, Peltola's second-round majority is misleading, since only 40% of the voters received their first choice of candidate, while 60% received either their second or third choice. Six out of ten voters voted for a Republican, but all ended up represented by a Democrat. It's hard to see how this is an improvement on plurality voting.
Unfortunately, there is no perfect voting system15. Every such system has its strengths and weaknesses, and a system needs to be chosen based on which strengths are most important and which weaknesses most need to be avoided. If the purpose of adopting the AV system was to prevent vote-splitting, it appears to have failed on the first try.
The special election was just to fill the congressional seat until this November when there will be another election for the usual two-year term. The same three candidates are expected to run again so that, unless one of the two Republicans drops out of the race, we may see a replay of what happened in the special election.
The result of the special election would have been exactly the same if the ballots had been counted using the old system, since Peltola won a plurality of votes. However, there wouldn't usually be two Republicans running for the same seat, though Begich might have been able to run as an independent. In addition, the new voting system was adopted by Alaskan voters in 202016, so it doesn't appear to have been part of some nefarious Democratic plot to split the Republican vote.
For these reasons, Republicans' complaints about AV voting seem misplaced. The problem is really with two Republicans splitting the party vote between them, rather than with the voting system itself. If the party wants to do something to stop a replay in the regular election, it should concentrate on convincing one of the two candidates to withdraw before November rather than whining that the vote is rigged.
- Winston Churchill, "The Worst Form of Government", The International Churchill Society, 11/11/1947.
- Elliott Davis Jr., "Palin Loses Special Election for Alaska House Seat", U. S. News and World Report, 9/1/2022.
- Nick Reynolds, "Republicans Blame Ranked-Choice Voting for Sarah Palin Loss: 'A Scam'", Newsweek, 9/1/2022.
- "Plurality System", Encyclopaedia Britannica, accessed: 9/8/2022.
- "Results of the 1860 election", Encyclopaedia Britannica, accessed: 9/8/2022.
- William Poundstone, Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It) (2008), p. 289.
- Poundstone, chapter 3: "A Short History of Vote Splitting".
- Michael Levy, "United States presidential election of 1992", Encyclopaedia Britannica, accessed: 9/8/2022.
- Candidates who split the vote are called "spoilers"; see: Poundstone, p. 289.
- Michael Levy, "Alternative Vote", Encyclopaedia Britannica, 9/1/2022.
- However, only some of these votes will be first-choice votes; others will be second choices, or third choices, depending on how many runoffs occur before a candidate reaches a majority.
- Poundstone, p. 287.
- "RCV Tabulation", Division of Elections, State of Alaska, 8/16/2022.
- "Alaska President Results", CNN, 12/2/2020.
- This is a simplified statement of Arrow's impossibility theorem; for a brief, non-technical explanation without a proof, see: John Allen Paulos, Beyond Numeracy: Ruminations of a Numbers Man (1991), under "Voting Systems".
- Eric Bradner, "How Alaska's ranked-choice voting system works", CNN, 8/31/2022.
September 4th, 2022 (Permalink)
Intimated or Intimidated?
An article in the spelling-challenged newspaper The Guardian1 about the tragic death last month of actress Anne Heche contained the following sentence: "Heche was stylish and smart–often radiating a sophisticated refusal to be intimated, which isn’t the same as cynicism."2 What does that mean? What exactly is "a sophisticated refusal to be intimated, which isn’t the same as cynicism"? What would an unsophisticated refusal look like? What would count as a refusal that is the same as cynicism? This sentence is a word puzzle.
I'm afraid that I can't completely solve the puzzle, but I do think that I can clear up one point of confusion. "Intimate" is most familiar as a noun and adjective but it's a verb in the sentence about Heche. As an adjective, it means "close", as in an "intimate friendship"; as a noun, it means a close friend. As a verb, it means to suggest or imply something, without stating it explicitly3. So, there's no way that the newspaper writer intended to say that Heche refused to be "intimated", since you can't "intimate" people.
Instead, the sentence should have read that Heche refused to be "intimidated" as "to intimidate" means to frighten someone into doing something4. So, Heche refused to be frightened into doing things, at least according to this article. These two words are spelled so similarly that they're sometimes confused, though their meanings could scarcely be more different.
None of the reference books that I usually check warn against confusing these two words, so this may not be a common error, but I've seen it before despite not now remembering exactly where. I suspect that the mistake usually goes only one way, that is, "intimidate" is misspelled as "intimate". Since the difference between the two words is only two letters, and they look very similar at a quick glance, it's an easy mistake to make.
As both words are English verbs, neither a spelling nor grammar checking program is likely to catch the substitution of one for the other. I tried the sentence in several online programs, and nothing happened except that one of the programs thought that "Heche" was misspelled.
So, the puzzling sentence should have read: "Heche was stylish and smart–often radiating a sophisticated refusal to be intimidated, which isn’t the same as cynicism." That makes it somewhat less puzzling, but I'm still not sure what it means.
- The newspaper is nicknamed "The Grauniad" for this reason, but you can't say it doesn't have a sense of humor about it, see: Elisabeth Ribbans, "Typo negative: the best and worst of Grauniad mistakes over 200 years", The Guardian, 5/12/2021.
- Peter Bradshaw, "Anne Heche was a little too stylish and smart for Hollywood", The Guardian, 8/12/2022.
- "Intimate", Cambridge Dictionary, accessed: 9/2/2022.
- "Intimidate", Cambridge Dictionary, accessed: 9/2/2022.
September 2nd, 2022 (Permalink)
Crack the Combination V
The combination of a lock is three digits long. The following are some incorrect combinations. Two of the digits in each incorrect combination are correct, but one is wrong:
- 879: One digit is in the correct position and one is in the wrong position.
- 381: No digit is in the correct position.
- 753: One digit is in the correct position and one is in the wrong position.
Can you determine the correct combination from the above clues?
Explanation: Because 8 is the only digit shared by combinations 1 & 2, it must be in the correct combination. Similarly, 3 must be in the combination because it's the only digit shared by 2 & 3, and 7 must also be a correct digit since it's the only one shared by 1 & 3. So, the correct combination is some permutation of the digits 3, 7 and 8.
To determine the correct order of the three digits, we have to look at the additional clues about position. We know, from the first clue, that either 8 is in the first position in the combination or 7 is in the second position. Let's examine the second possibility.
Suppose that 7 is in the second position in the combination. Then, 8 is in the wrong position in clue 1, which means that it must be in last place. So, 3 must be in first place, by elimination, making the correct combination: 378. However, this cannot be correct since it would mean that 3 is in the right position in clue 2. So, our hypothesis that 7 is in the second position must be wrong, which means that 8 must be in the first position.
So, 7 cannot be in the middle position, meaning that it must be in last place. This leaves the middle position for 3, by elimination, making the correct combination: 837.
WARNING: May cause dizzyness or confusion. Alcohol may intensive this effect.
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