The Guardian: Can you solve it? Are you smart enough for MIT?
I have a 12 year old, maths head of a daughter, who has MIT or CalTech aspirations. I will show her this article this week. I have found out recently, that if she’d like to study maths at MIT, she needs to be one of the UK’s top mathematicians! No pressure!!!
In 1966, MIT student Allan Gottlieb published his first Puzzle Corner in the MIT Technology Review.
More than half a century later, Gottlieb – who has been a computer science professor at New York University since 1980 – continues to publish Puzzle Corner in every issue.
The column has legendary status among maths puzzle nerds. Most of the problems are too technical for a non-specialist audience but the column always includes a quickie, which he calls the Speed Department. Here are four word-based conundrums I’ve selected from the last decade.
1. What is the numerically largest Roman numeral that is a normal English word?
Solution: MMM = 3000 is in the dictionary app in my computer, and is allowed in Scrabble, so I think it wins. The Shorter OED only has MM = 2000. If you think that interjections/exclamations don’t count as ‘normal’ words, the next best I think is MID = 1499
2. How do you prove literally that 11 + 2 = 12 + 1?
Solution: If you write out each side of the equation as words, you will discover the curious fact that ELEVEN AND TWO is an anagram of TWELVE AND ONE.
3. The 9-letter word SPLATTERS has an intriguing property. You can remove a single letter to make an 8-letter word, without rearranging the other letters. You can remove another letter to make a 7-letter word, and then a 6-letter word, and so on down to a single-letter word. At no stage is the order of the letters rearranged.
splatters, splatter, platter, latter, later, late, ate, at, a.
Find two other 9-letter words that share the same property. As a (kosher) hint, the words pig and sin appear as the 3-letter words. (Remember: at no stage do you ever change the order of the letters.)
Solution: Here are the two I was thinking of. If you have found any more, please post them below the line.
sparkling, sparking, sparing, spring, sprig, prig, pig, pi, I.
startling, starting, staring, string, sting, sing, sin, in, I.
4. What is special about 8,549,176,320?
Solution: The clue was in the text when I said that all these puzzles were ‘word-based.’ If you write out the words for the digits, and read them alphabetically, you will describe the above number.
Eight, Five, Four, Nine, One, Seven, Six, Three, Two, Zero.
Thanks to Allan Gottlieb for permission to use today’s puzzles.
In other news, I’ve just read The Rules of Contagion by the mathematician and epidemiologist Adam Kucharski, which is out this week. The book is a brilliant and accessible guide to the maths of outbreaks, from diseases to internet memes. The subject could not be more topical. Indeed, Adam, who is based at the London School of Hygiene & Tropical medicine, is currently working on analysis to support the global response to coronavirus. A recommended read.