CTK Insights

Indeed, is it possible to miss the New Year moment? The question is not meant to account for a possible tragic circumstance and is being asked plainly and candidly. Assuming you are in good health on December 31 of one year and remain healthy on January 1 of the next year, is it possible to [...]

I am not sure who coined the term "The Star of David Theorem" to designate the identities discovered in the early 1970s. There are in fact two of them, both related to the "Star of David" configuration in Pascal triangle (The diagram is courtesy wikipedia.org.) The first result discovered by Hoggatt and Hansell in 1971 [...]

This puzzle comes from a wonderful Russian site, where its solution is presented as a sequence of animations. Is it possible to wrap the cube with a 3×3 piece of paper below it? Handling of the paper is subject to two conditions: The paper may be only cut or folded along the crease lines. The [...]

Nowadays, finding the area of curvilinear shapes falls in the purview of calculus. But the problem of finding areas draw much interest in antiquity and preoccupied mathematicians ever since. One of the acknowledged results by Hippocrates of Chios (470-410 B.C.) is the Squaring of a Lune. The problem of squaring a shape refers to a [...]

(Borrowed from http://www.boingboing.net/2011/03/21/how-to-make-a-hamant.html)

You have to see it to believe it.

The FLT - Fermat's Last Theorem - states that for n ≥ 3, the Diophantine equation xn + yn = zn has no solutions. We now know this is true due to the 1995 result of Andrew Wiles. The theorem was conjectured by Pierre de Fermat in 1637 and thus withstood the many attempts during [...]

A combinatorial result due to Paul Erdös and John Selfridge has been discussed by R. Honsberger in his In Pólya's Footsteps. The problem was also included by Savchev and Andreescu in the wonderful Mathematical Miniatures. I reported these results elsewhere. More recently an extension of the discussion was posted in the problem section of the [...]

Sam Loyd's Fifteen is a famous conundrum from the end of the 19th century. As the recent investigation by Jerry Slocum and Dic Sonneveld has revealed, attributing the puzzle to Sam Loyd is justified only partially. Repeated claims to the contrary notwithstanding, Sam Loyd has not invented the puzzle. He is certainly responsible for creating [...]

Three ropes have been fastened to a horizontal plunk, tangled a little as if one tried to make a braid and, lastly, loosely attached to an auxiliary plank to keep them braided. Down below there is a third plank. The task is to attach three additional ropes to the first ones at one end and [...]