The text is about a homework assignment given by the author to her students, involving a famous Russian joke about a race between a Russian and an American car. The joke is that the Russian newspapers truthfully reported that the ...
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The text discusses generalizing the game of SET using different groups and defining a set as a few cards that might need to be in a specific order that multiply to the group’s identity. It explores different examples of groups and...
Foams are 2-dimensional CW-complexes embedded in 3-space, with singularities only of the most generic kind, which makes them relatively simple. They are combinatorially defined, which makes them easier to work with than with many ...
The text discusses various interesting properties of the number 2025, including its classification as a composite, deficient, evil, odd, square, and powerful number. It also explores its connection to apocalyptic power and its rel...
The text discusses a puzzle about identical twins and the probability of their genders. It also explores the rare occurrence of identical twins being of different genders due to errors during splitting of the fertilized egg.
The text presents a puzzle from the Möbius tournament for middle school students, asking for which natural numbers n greater than 1 it is possible to arrange n numbers 1 through n in a circle so that the difference between two nei...
The blog post discusses a new hat puzzle from Gribalko, which is reminiscent of traffic lights. It presents a puzzle where seven mathematicians have hats placed on their heads, and they need to determine the color of their own hat...
The blog post discusses a puzzle involving arranging four matches to form a plus sign and then moving one match to create a square. The author shares the different solutions that were discovered, including the one she came up with...
The blog post discusses the game of SET and its generalization to groups. It explains how the game works, how it can be generalized to a group, and how different variations of the game can be played using different groups. It also...
The blog post discusses the concept of foams, which are finite 2-dimensional CW-complexes with extra properties. The author explains how to construct a finite 2-dimensional CW-complex and the additional properties that foams have....
The blog post discusses a riddle where the number 20 is used three times to make 60, and then challenges readers to use a different number three times to make 60. The author shares various inventive solutions from her students, in...
Tanya Khovanova shares a puzzle from her friend Alexander Karabegov, which involves finding all solutions of the equation g(g(x)) = x. She was impressed by his solution, which only uses quadratic equations. She gives a brief overv...
The blog post discusses an interesting homework puzzle about two sisters who clean a shed and end up with one sister having a dirty face and the other a clean face. The post includes different answers to the puzzle and a humorous ...
The blog post discusses a story about Sam's locks and how he uses them to protect himself from burglars. It describes how Sam's locks are not completely identical and how he randomly picks which ones to lock. The post also mention...
The blog post discusses a hat puzzle where a sultan tests his three sages by placing hats on their heads, with one sage being color-blind. The sages are asked if they know the color of their hats, and the conversation unfolds with...
The blog post discusses a physics puzzle about a fisherman needing to move a heavy iron thingy from one river’s shore to another. The expected answer is to attach the thingy to the bottom of the boat. The post also includes invent...
The blog post is about Tanya Khovanova's experience attending the Gelfand seminar before moving to the US. She took some pictures at the seminar and recently decided to digitize them. The seminar was a significant part of her life...
The blog post discusses the term fibonometry, which describes a parallel between trigonometric formulas and formulas with Fibonacci and Lucas numbers. It mentions the work of John Conway and Alex Ryba, as well as the author's expe...
The blog post discusses a Fibonacci trick where the sum of the first 10 terms of a Fibonacci-like sequence can be calculated by multiplying the 7th term by 11. The author also mentions a generalized version of the trick and the re...
The blog post is about a math problem involving averaging adjacent numbers. The author discusses the problem and provides a proof that 2^-9 is the best possible solution. The post includes comments from readers and their interpret...
The blog post discusses the 5-card, 4-card, and 3-card tricks in magic. It explains the strategies behind these tricks and how they can be performed using a standard deck of cards. The post also mentions the introduction of a more...
The blog post discusses the famous 5-card trick and the information theory underlying it. It explores the mechanics of the trick and the information-theoretic argument behind it. The post also presents a more direct, intuitive arg...