It had been my understanding that the early universe was too hot to sustain _________ hydrogen for the first half-billion years or so, and was therefore a necessarily opaque plasma of protons and electrons.
On October 11, some 60,000 _________ grocery workers at 852 stores in southern California went on strike or were locked out of their jobs.
That's a question we will all be debating this year when contract negotiations open between _________ nurses and the government.
Previous studies have shown that the _________ ammonia molecule and not the ammonium ion is the form of the toxicant harmful to fish.
These four sentences, taken from different webpages, illustrate some of the uses of a certain 9-letter word… or perhaps I should say multiple 9-letter words that happen to be spelled (but not pronounced) alike. To prevent confusion, a hyphen is sometimes added. What's the word?
Yesterday's Puzzle + Solution
Shakuntala Devi was known for her feats of mental calculation. See the video for an example!
While Devi's abilities were exceptional, many of her tricks (which she revealed in her book Figuring) were based as much on mathematical insight as raw brainpower. You too, if you knew what she knew, could determine (an integer) with almost no effort.
Well? Can you?
As a hint, the first few 5th powers are provided in a table at right.
(no calculators lol)
Solution
Separate the radicand into two blocks of 5 digits: 20730 71593. The first block is between 75 and 85, which tells us that the root has a tens digit of 7. The second block ends in 3; the units digit of the root is the same. Hence the answer is 73.
This method finds the 5th root of any 6- to 10-digit fifth power; I leave it to you to figure out why it works.
Devi was a pretty cool person! I knew about her growing up—someone who could do speedy calculations was my first, distorted image of a "math genius"—but I only recently learned more about her life. After discovering that she was married to a gay man, she researched and wrote a book urging full social acceptance of homosexuality. This was in the 1970s, when that was not a common stance to say the least.
Oh, and lest you think all her calculating skills can be demystified as in yesterday's puzzle: she once took the 23rd root of a 201-digit number in under a minute. No, I don't know how.
Congratulations to yesterday's solvers Jacob C., Mr. Gregg, Kate, and Dr. Hill. Thanks to everybody who made a guess!
About This Site
Though he now teaches mathematics, Dr. (né Mr.) Shapiro's first job in a K–12 school was as a lunch monitor in Davis, CA. It was there that he originated the Puzzle of the Day, even rewarding correct answers with tickets in denominations like "15 points" (though without a clear idea of how he'd ultimately redeem these). Dr. Shapiro's favorite puzzle from this pre-professional era was "Tell me the location of the beehive on this campus."
Ten years later, Dr. Shapiro revived Puzzle of the Day at Proof School, writing each day's puzzle on a name tag. After 600 puzzles or so, he was just starting to feel normal about students reading his chest all the time when campus closed and the puzzle, like the rest of our lives, moved online. New puzzles are posted daily on school days.
Want to catch up on old PotDs? There's an archive currently containing puzzles from March 2020 to March 2021.
Shakuntala Devi was known for her feats of mental calculation. See the video for an example!
(an integer) with almost no effort.