Do you know that I participated in Linguistics Olympiads in high school? They are not well-known in the US, but the Soviet Union has been running them since 1965. The first International Linguistics Olympiad was conducted in 2003, and the US joined in 2007. They are called Computational Linguistics because you are expected to discover some phenomenon in an unfamiliar language on the fly instead of knowing a lot of languages already. The problems mostly need logic and are a good fit for a person who likes mathematics. However, a feel for languages is very helpful.
I do not remember why I started attending the Olympiads, but I remember that there were two sets of problems: more difficult for senior and less difficult for non-senior years. I used to be really good at these Olympiads. When I was in 8th grade, I finished my problems before the time ran out and started the senior problems. I got two awards: first place for non-senior years and second place for senior years. In 9th grade, I got two first-place awards. I didn’t know what to do in 10th grade, which was a senior year at that time in the USSR. I couldn’t get two first-place awards, as I could no longer compete in the non-senior category. I felt ashamed that my result could only be worse than in the previous years, so I just didn’t go.
The prizes were terrific: they gave me tons of rare language books. In the picture, a guy from the jury is carrying my prizes for me. I immediately sold the books at used-books stores for a good price. Looking back, I should have gone to the Olympiad in 10th grade: my winter boots had big holes.
What do you give a mathematician who likes only mathematics if you want to expand her geographical horizon? I just got such a gift: A math book that made me feel that I was in Australia. The book, A Dingo Ate My Math Book: Mathematics from Down Under, written by Burkard Polster and Marty Ross, has lovely essays, nice pictures, and a strong Australian flavor.
2022 is abundant, composite, even, evil, square-free, and untouchable.
In addition, 2022 is the smallest number n such that n, n+1, n+2, and n+3 have the maximal exponents in prime factorization equal 1, 2, 3, and 4 correspondingly. Indeed, 2022 = 2·3·337, 2023 = 7·172, 2024 = 23·11·23, and 2025 = 34·52.
Problem. The numbers 22021 and 52021 are expanded, and their digits are written out consecutively on one page. How many total digits are on the page?
My daughter was talking at her kindergarten about what her parents do for work. She said that her mom catches bugs, invokes demons, and talks to clods.
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I have neither Twitter nor Instagram. I just go for a walk to tell strangers what I ate and drank and how things are at work and at home. I have three followers: a doctor and two policemen.
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Life is like Rubik’s cube: fix one side, better not look at the rest.
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My Roomba just devoured a piece of cheese I wanted to pick up and eat. The war between humans and robots is already here.
My friend, John Conway, had a trick to help him with tricky situations. Whenever he needed to make a non-trivial decision, he would ask himself, “What would John Conway do?” As he explained to me, he had in mind the public image he himself created. He liked the image and thought this mental trick helped him be a better, more productive, and not-to-forget, flashier person.
From time to time, I catch myself in need of a decision and ask myself, “What would John Conway do?” And he gave me the answer: I should change the question and ask myself, “What would Tanya Khovanova do?”
Here are some snowball sentences suggested by my students.
I do not know about radon’s, osmium’s, polonium’s abilities.
I am the only short person playing football.
“I am not even smart,” mother remarks.
I do not know where people acquire insanity.
“A no,” Joe said while eating burgers mightily adultlike.
I am not very happy during Mondays.
I do not joke.
I be—arr, mate—avast!
I do not know super skates.
I do not fear yucky cheese; however, kamikaze elephants jackhammer lumberjacks blackjacking backpedalling brontosauruses, artificializing territorializing icositetrahedrons.
Can you invent some other snowball sentences? But first, you need to figure out what they are.
Each year I look at the MIT Mystery hunt puzzles and pick ones related to mathematics, logic, and computer science. I usually give additional comments about the puzzles, but this year’s titles are quite descriptive. Let’s start with mathematics.
I recently wrote a post, A Splashy Math Problem, with an interesting problem from the 2021 Moscow Math Olympiad.
Problem (by Dmitry Krekov). Does there exist a number A so that for any natural number n, there exists a square of a natural number that differs from the ceiling of An by 2?
The problem is very difficult, but the solution is not long. It starts with a trick. Suppose A = t2, then An + 1/An = t2n + 1/t2n = (tn + 1/tn)2 − 2. If t < 1, then the ceiling of An differs by 2 from a square as long as tn + 1/tn is an integer. A trivial induction shows that it is enough for t + 1/t to be an integer. What is left to do is to pick a suitable quadratic equation with the first and the last term equal to 1, say x2 – 6x + 1, and declare t to be its largest root.