Hello 2020! It’s been 3 years since my last post (3 years!!). It would’ve been poetic if I posted on Dec. 2, 2019 with a third rendition of “Where has the time gone?” but alas, I missed that opportunity last year. But, regardless, I am back! Perhaps when I am not chugging through paper deadlines, I will make a post of what has kept me from blogging for such a time (if I, myself, even know…).
Now, onwards with our scheduled program…
For my paper of the day, I feel obligated to first report on the now #oldnews of 2019 regarding the resolution of the Sensitivity Conjecture by Hao Huang. As countless other blog posts have stated, this result is truly extraordinary and I encourage all of you to read Huang’s elegant proof. The main proof is only 3 pages (3 pages!!).
Now, the puzzle.
I’ve been reading this book called The Moscow Puzzles by Boris A. Kordemsky (Edited by Martin Gardner) as a method of de-stressing from my deadline chugging. There are many nice puzzles in this book and certainly ones that require quite a bit of ingenuity (and the prose is also hilarious at times). For those who have done contest math, although some of the problems may seem easy, I still encourage you to read the book since there are lots of problems that are different in style from those that appear in contests.
I particularly liked the following puzzle from the book:
A work train, made up of a locomotive and 5 cars, stops at a small station. The station has a small sliding that can hold an engine and 2 cars.
A passenger train is due. How do they let it through?
Pg. 34 of The Moscow Puzzles
The reason why I liked this puzzle was because the first reaction I had was: The problem is poorly defined. What can the train do, can it go backwards, CAN IT FLY? And then, I realized I’ve worked for too long in TCS, and it is an important life skill to know that trains can, in fact, go backwards… Highlight the below space for the answer:
Copied verbatim from The Moscow Puzzles: The work train backs into the siding, which can hold its rear 3 cars. Uncoupling them in the siding, the rest of the work train goes forward a sufficient distance. The passenger train comes up and couples on the 3 cars left by the work train. It backs up on the main track. The work train backs up into the siding, which will now hold its engine and the remaining 2 cars. The passenger train uncouples the 3 cars it took from the siding and goes through.