IBM Research

- Ponder This This puzzle was suggested by Hugo Pfoertner - thanks Hugo! In a now-famous 2004 article, Ben Green and Terence Tao proved that arbitrarily long arithmetic progressions exist in the primes. This holds true analogously for other sets of numbers if their density is sufficiently high, for example, numbers that are the sum of two squares. There are also enough numbers of the form x² + y²…

Imagine a cataclysm wipes out humanity's scientific knowledge. Hard drives, the internet, books, movies — all about to be lost. But before everything is gone, you have the chance to leave a single sentence for future generations. What would you write? Physicist Richard Feynman once answered that hypothetical saying he would tell the future of humanity that all things are His full quote, trying to…

- Ponder This The Wheel of Buttons This puzzle was suggested by Sanandan Swaminathan - thanks! A game show is arranged as follows: The main attraction is a wheel that has buttons equidistant from one another, such that the wheel looks perfectly symmetric. Each button has two possible states: "on" and "off". There's no indicator to the status of a button, and each press toggles between those two s…

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