What’s wrong with diagonal thinking, anyway?

Last week, we were talking about “lateral thinking” puzzles, taking a board game called Brain Strain as a jumping-off point. But it wasn’t my first encounter with them, which is probably the reason I have so many opinions. In fact, I remember where I first came across this sort of thing: it was in a book called The Amazing 1000 Puzzle Challenge (Allen, 2004), within which over 900 of the puzzles¹ are the sort of thing you might find in an IQ test.² Some of the others are what you might call “classic” puzzles, like crosswords, wordsearches and mazes; no sudoku, though, since this book came out in the year they made their debut in Western newspapers.³ But scattered in between all these were some puzzles the likes of which I hadn’t seen before, and which I was fascinated by. I left you with an example from the book at the end of the last post.

A family of four were going on a mountaineering holiday. The second morning they were all found dead in their cabin. The coroner declared that they had all died from drowning. The faucets in the cabin had not been left on and the boiler and water storage units were undamaged. There was no sign of any foul play. What caused them to drown?

I wasn’t quite fair to you—or to the book—when I quoted this, because a distinctive feature of these puzzles as they appear in this book is that they typically include a numbered list of extra details to help you out, and maybe rule out some other things you might have thought of.

1. They were a mile from the nearest lake.
2. It had not rained for five days. This wasn’t a flash flood.
3. It was not caused by problems with a dam.

Damn. This does shut down the puzzler’s creativity a bit, but I suppose it helps to ensure that there’s only one correct answer. “Helps”, but I don’t think it completely solves the non-uniqueness issue: for instance, these are not the answer the book was looking for, but things I’ve (as last time) just made up.

• The cabin roof cracked under a build-up of heavy snow, causing a deluge of snow which quickly melted in the warm cabin.
• Nothing says they drowned in water: the fuel tank could have burst, flooding the cabin with petrol.
• It says there was “no sign” of any foul play, but maybe the foul play was just very stealthy?

Yeah, alright, those aren’t my best efforts; maybe the most convincing answer this time really is the one the book gives.

They were travelling to their destination by cruise ship.

Oh, right; they never said it was a mountain cabin, and they said they were far from a lake but not from the sea. Maybe this one is fine… Oh, wait, you’re not done, book?

They were travelling to their destination by cruise ship. The hull of the ship was rammed during the night, and their cabin was below the water line. The pressure of the water held the door shut, they could not escape, and the rescuers were too late to save them.

Maybe I’m just not big-brained enough,⁴ but I don’t think you can conclude all of those details from the puzzle as given.

I was rather impressed with these back in the day, so much so that, when I gave the humongous book away to make room in my childhood bookcases, I typed out some of the puzzles of this kind so I could keep hold of them.⁵ But I don’t think I solved any of them. I think what I enjoyed was reading them, reading the answers, and then asking other people. And, honestly, I don’t think I was wide of the mark. I assert that these sorts of puzzles aren’t really designed as puzzles to be solved—they’re designed as puzzles to be asked, so that the person asking them can feel superior when they give the “obvious” answer.

The more you look at these things, the more you notice certain recurring ideas. We’ve already seen one, which is an obsession with death—continued with the drowning puzzle this week, where the answer reads like the author’s fantasy about the grim demise of a family who have personally wronged them. But the other thing we spot is a certain, shall we say, “traditional” outlook on life.

Quite a few of them only work as trick questions—sorry, “lateral thinking puzzles”—if the person hearing them makes the assumption that “person” = “man”, which you may have heard as a solution to the “barber paradox” (if the barber shaves every man in town who doesn’t shave himself, who shaves the barber?). The board game we discussed last week has one (Lagoon Games 1995):

Two miners were sitting on a bench. One miner was the other one’s son, but the other one was not his father. Why?

You don’t have to be a man to be a miner any more? Next you’ll be telling me that you don’t have to be in a brass band either!

To prove that’s not a one-off, I’ll cite another; this one comes from The Puzzle Challenge (Mensa 2005),⁶ where the riddle is far too long to bother writing out in full. It involves a “Wild West” setting, in which “there [a]re five men present” at a card game; where the dealer at cards has shot someone dead, but the sheriff is “unable to arrest any of the men who had taken part in the game”. “There were five men present, but the dealer was a woman” says the answer, and you can almost picture the smug smile on the face of whoever has just read you the puzzle as they read that out.

A generous interpretation of this is that the puzzle is inviting you to challenge your own internal biases—why can’t the dealer be a woman? I’d love it if that were the intent. And maybe it is, but, if so, it’s a shame these things can’t extend that to other internal biases you might have.

See, when I was looking through these books, one thing that struck me was how many of the puzzles involved exoticised depictions of other cultures—which, adding insult to injury, are often completely superfluous to the puzzles themselves.⁷ Here’s one from my old childhood favourite (Allen 2004):

Once, in India, a queen owned two horses and used them to help destroy a neighbouring king. There was a hard fought battle in which all the king’s men were killed. When the battle was over the victors and the vanquished all lay side by side in the same place. Explain.

Unusually for this book, no supporting hints are given, but it doesn’t matter—it’s pretty obvious (I think) that the answer is that it’s a game of chess. I guess chess originated in India, so that’s why the puzzle is set there? Hmm. Well, what about this one from The Puzzle Challenge (Mensa 2005)?

Khalil ben-Omar became Calif of Baghdad. Shortly after taking up his new position one of his advisors pointed out to him a little scruffy fellow riding a donkey in through the city gates. “That man,” said the advisor, “is a trader from Pakistan. […]”

We’re going to stop there, for two reasons:

• The puzzle itself is one of the most stupid ones I’ve seen, and by now I’ve seen a lot of these. You have to work out how the man is getting rich from smuggling, when all he does each day is ride in and out on a donkey without any wares. The “answer” is that he’s smuggling donkeys. But in that case he smuggles exactly as many donkeys in as he smuggles out, so—how is he making money, exactly?
• More to the point, in an attempt to put this in a vaguely Asian setting, the author has got rather historically muddled. The last Caliph of Baghdad was al-Musta’sim bi-llāh, whose rule ended with the Mongol conquest of 1258 (Wikipedia 2004a). The word “Pakistan” was first coined by Choudhry Rahmat Ali in 1933 (Wikipedia 2004b). And yes, I know it’s bad academic practice to cite Wikipedia, but I do it to prove just how easy this stuff is to fact-check.⁸

Fact-checking is also not always these books’ forte, which I find a bit much given the number of these puzzles I’ve come across which actually aren’t of either of the two types I mentioned last week—neither one with several plausible answers, nor one relying on grammar—but in fact can only be solved if you know a specific general knowledge fact.⁹ This one asks a lot of its reader while offering little in return (Pickering 2004).

The spy satellite tunes in to conversations from Ecuador but not Egypt, Zaire but not Zambia. Which of these countries will it listen in to:

• Bolivia
• Borneo

Like I said last week, I’ve read a lot of these now, so I know how they work. The answer has to be Bolivia, because Borneo isn’t a country:¹⁰ it’s an island shared by three countries: Brunei, Indonesia and Malaysia. Unfortunately, though, Borneo is the answer the book is looking for, because the answer is that the satellite only listens in to countries on the equator.¹¹

That’s another flaw with these things: lack of internal consistency, sometimes even within the same book. For example, here’s one from Mind-Bending Lateral Thinking Puzzles (MacHale 1997).

Most English words are quite short, although words of 15 letters or more aren’t impossible. What is the longest word in the English language?

You might have seen this one before, because it’s a bit of a classic—a variant of it was mocked by an early xkcd comic strip (Munroe 2006). The first sentence is misdirection; the answer is just “language” as the longest word in the phrase “the English language”.¹² So you should now easily be able to take on this one, two pages later in the same book.

How many times does the letter “f” occur in the following sentence? Friends will not follow your advice if they feel that your words are full of flattery!

If you said “one”, because there’s only one in the phrase “the following sentence”, good logic! Unfortunately, logic will not help you here—which is, at least, consistent with de Bono’s argument in The Use of Lateral Thinking, where he contrasts logical, “vertical” thinking with the lateral thinking he proposes (de Bono 1967). No, for this one you were supposed to count “f”s, of which there are seven. I think the “lateral” bit is supposed to be that the ones at the end of “if” and “of” are easy to miss? If so, I have to hand it to them, because it took me ages to find all seven even when I’d read the answer. But that didn’t make me appreciate it any more.

Of course, one reason you might keep moving the goalposts like this is to keep the puzzler on their toes. But then you’re not setting a fair challenge, to get satisfaction from the joy of the reader when they solve it; your satisfaction instead comes from telling them the “right” answer when they’ve already failed. That doesn’t make you clever; it makes you a little obnoxious.

Think I’m being uncharitable myself? Sure, you can think that. But let me leave you with one more quote from The Puzzle Challenge (Mensa 2005), where I think the mask slips.

This is a puzzle which is much more fun if you try it on an unsuspecting victim.

Now, if they’d just come out and said that for all of them, we could have saved a lot of time.

References

Allen, Robert, ed. (2004), The Amazing 1000 Puzzle Challenge (Kettering: Index Books).

de Bono, Edward (1967), The Use of Lateral Thinking (London: Jonathan Cape).

Lagoon Games (1995) Brain Strain: The Lateral Thinking Game (cards) (London: Lagoon Games).

MacHale, Des (1997), Mind-Bending Lateral Thinking Puzzles (London: Lagoon Books).

Mensa (n.d.), ‘About Mensa’ [web page], accessed 17 April 2026.

Mensa, Robert Allen, Dave Chatten and Carolyn Skitt (2005), The Puzzle Challenge (London: Carlton Books).

Munroe, Randall (2006), ‘Words that End in GRY’ [web comic], xkcd, 11 October, 169, accessed 17 April 2026.

Pickering, Fran (2004), Lateral Thinking Puzzles, Beat the Timer (London: Lagoon Books).

Teletext: C4 East Midlands (2005), ‘Sudoku’, 2nd September, 142.

Wikipedia contributors (2004a), ‘Al-Musta’sim’, Wikipedia (last modified 17 December), accessed 17 April 2026.

Wikipedia contributors (2004b), ‘Pakistan’, Wikipedia (last modified 31 December), accessed 17 April 2026.

1. I think. I haven’t actually counted. ↩︎
2. Don’t even get me started on IQ tests. ↩︎
3. One thing that I was surprised to learn did overlap with sudoku was teletext, which I had thought was already dying by 2004. Perhaps it was, but it didn’t stop Teletext on Channel 4 from including a daily sudoku “[Y]ou may want pen and paper at hand to copy the grid”, viewers were advised (Teletext 2005). ↩︎
4. This book does, at least, have the grace to have an introduction that says “There is a theory that being good at puzzles proves you are a being of superior intelligence. This is pure piffle” (Allen 2004). ↩︎
5. And then I bought the book again this year so I could write this post properly, because the National Library of Scotland didn’t seem to have it. ↩︎
6. This book, unfortunately, came the closest to proving that the problem is me. When I was looking for the answer to puzzle 16, I turned to answer 16, but that made even less sense than normal. I turned back to the puzzle, and saw that it said “See p. 98, answer 9”. “Ohhh,” I said to myself, “they’ve mixed up the answers so its harder to spoil the puzzles.” I then turned to answer 98, and wondered why that didn’t make any sense either. ↩︎
7. Or, put another way, you could often write the same puzzle with the same “trick” to answering it with the offending description removed. ↩︎
8. “But you’re being unfair!” I hear you shout. “In 2005, Wikipedia was four years old. Those facts might not have been there back then!” Nope: if you look carefully at my reference list, I’ve cited the articles as they stood on 1st January 2005, when all that information was indeed included. Also, this book is by Mensa, for heaven’s sake. If an organisation founded as “a society for bright people” (Mensa “About Mensa”) can’t be held to high academic standards, who can be? ↩︎
9. Examples of things you need to know for some of these are: that white feathers were a symbol of cowardice in the First World War; that air is colder above the equator than above the poles; that the de Havilland Comet was filled with water to simulate high-altitude flight conditions; and that, in the army, captains don’t lead battalions (Allen 2004, Mensa 2005). In this latter one, you’re also asked to assume that a young child would know this despite “[knowing] little about the war” in question. Plausible! ↩︎
10. Incidentally, by 2004, neither was Zaire; it had been renamed back to the Democratic Republic of the Congo seven years previously. ↩︎
11. It’s not hard to think of a reason why the answer would be Bolivia even if we ignore the “country” thing. Maybe it only listens in to places with more vowels than consonants in their names. ↩︎
12. I think this sort of thing is a bit unfair, because grammatically you need to put quotes around the phrase to identify that you’re talking about the phrase itself, rather than the thing it represents—as indeed I did when explaining it. That said, that exact trick is the basis of cryptic crossword puzzles, two of which I’ve published on here, so it would be rather hypocritical of me to then pull them up on it. ↩︎