Gizmodo Monday Puzzle: Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo

If you haven’t seen before why eight ‘buffalo’ strung together form a valid English sentence, then strap in for a linguistic trip. Buffalo has at least three meanings: as a collective noun it refers to bison, as a proper noun it’s a city in New York, and as a verb it means to bewilder. The eight-buffalo sentence uses all three meanings, so let’s decipher it by substituting each with a similar word. We’ll use ‘bulls’ for the animals, ‘French’ for hailing from France, and ‘bewilder’ for the verb. With this translation,

Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo

becomes

French bulls French bulls bewilder bewilder French bulls.

Okay, not much easier to understand. Largely because the sentence omits some implied words:

French bulls (who other) French bulls bewilder (then go on to) bewilder (yet another group of) French bulls.

The sentence says that bulls who get bewildered by other bulls then go on to bewilder yet more bulls, and also all the bulls are French. The eight-buffalo construction is really commentary on the never-ending cycle of animal bewilderment in upstate New York.

The neat sentence almost always appears in this eight-word form, but amazingly you can string together any number of buffalo to form a valid sentence! From the single “Buffalo!” exclamation of an animal sighting, to the double “Buffalo buffalo” observation that bulls tend to bewilder, all the way to a thousand buffalo in a row.

To see this, suppose you have a string of n buffalo and it forms a valid sentence. If any of your animals don’t already hail from New York, then you can extend the sentence by inserting a Buffalo (turn a bull into a French bull). But if all of your bulls are already French, then you can change one French bull to “bulls that other bulls bewilder.” Repeating these transformations generates longer and longer grammatically correct sentences.

The phenomenon works with any word that can triple as a collective noun, verb, and adjective. Another example is “police,” which refers to officers of the law, the act of enforcing that law, and a town in Poland.

Try to wrap your mind around more grammatical oddities below.

Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you haven’t solved last week’s yet!

Puzzle #42: Grammatically Correct

Some of these are famous questions, so if you’ve seen them before, then please refrain from answering in the comments to give newcomers a shot.

Punctuate the following so that they make sense:

1. that that is is that that is not is not is that it it is
2. James while John had had had had had had had had had had had a better effect on the teacher

Below, fill in the three blanks with the same letters in the same order so that the resulting sentence makes sense. You may add spaces between letters as needed:

The ____ doctor was ____ to operate on the patient because there was ____.

For example, “I ____ wish my doctor would tell me ____ when she was free for an appointment” could be completed with “sometimes” and “some times,” respectively.

I’ll be back Monday with the answers and a new puzzle. Do you know a cool puzzle that you think should be featured here? Message me on X @JackPMurtagh or email me at gizmodopuzzle@gmail.com

Solution to Puzzle #41: Time Warp

If you managed to solve last week’s difficult clock puzzle, then you may have too much time on your hands.

If you swap the hour hand and the minute hand on an analog clock, how many possible valid times can it still display?

Quick aside, in case what I meant by “valid time” was not clear in the problem statement: not all possible positions of the hands actually occur on a normal functioning clock. For example, there is never a moment during the day when both hands point directly at the 3. Because at 3:00, the hour hand points at the 3, but the minute hand points at the 12. At 3:15, the minute hand points at the 3, but the hour hand is now a quarter of the way to the 4. Hand positions that actually occur on a typical functioning clock I’m calling “valid.”

The answer to the puzzle is 143. There are a few ways to tackle this. I think the explanation below is pretty slick, but for a more detailed mathematical approach, check out Enfy’s solution in last week’s comments.

We want to know for how many positions of the hands on a typical (unmodified) clock can we swap the two hands and still display a valid time. Note that on clocks, the minute hand moves 12 times faster than the hour hand (when the minute hand completes one revolution, the hour hand moves one twelfth of the way around the clock face). Our trick will be to imagine adding an extra hand that moves 12 times faster than the minute hand. This effectively models two different clocks at once: The hour hand and minute hand behave like a normal clock while the minute hand and extra hand behave like a sped up clock, but because their relative speed is preserved (one moves 12 times faster than the other) they still form all of the same positions as a normal clock with the minute hand taking the role of the hour hand.

So we have one clock where the minute hand behaves like a minute hand, and another one where the minute hand behaves like an hour hand. On this view, the interchangeable times occur whenever the hour hand and the extra hand overlap. The true hour and minute hands always form a valid time, and if we swap them when the hour and extra hand overlap, then the minute hand assumes the role of the extra hand (which was acting like a minute hand) while the hour hand assumes the role of the minute hand (which was acting like an hour hand).

The extra hand moves 144 times faster than the hour hand (12 x 12). They begin overlapping at noon, and then every time the extra hand does one revolution, it will overlap with the hour hand once. The last of these overlaps will occur at midnight, which in our stipulations we’re not counting as distinct from noon. So the number of valid times is 143.