![]() In fact, if you want a stiffer challenge, try doing this puzzle entirely in your head. If you squeeze the last drop of deduction from the puzzle conditions, you won’t have too many trial-and–error candidates to search through. In this case, you can use the tricks you learned in school for determining if a number is divisible by a given digit. All digit substitution puzzles of this type can be solved with a two-step process familiar to those who’ve solved a sudoku puzzle - first you deduce relationships between the digits, which narrows the possibilities, and then you do a systematic trial-and-error search for the unknown digits. I urge you to do it using pencil and paper. You can solve this puzzle by performing a brute-force search with a computer, of course, but you don’t need to. For me as a puzzle maker, this digit substitution puzzle inspires the same feeling that Mozart inspired in Einstein, who said that Mozart’s music “was so pure that it seemed to have been ever-present in the universe, waiting to be discovered by the master.” Only someone as numerically gifted as Conway could have plucked such a perfect Platonic form from puzzle heaven! And then to have this natural set of conditions yield a unique answer is amazing. Once you read the first two conditions, you know exactly what the rest of puzzle is going to be. It flows completely naturally, without an iota of arbitrariness or artifice. Each of the digits is different, and they have the following properties:īefore you begin this puzzle, take a minute to admire the absolute perfection of its form. There is a mysterious 10-digit decimal number, abcdefghij. Finally, we’ll immerse ourselves in an open-ended game contributed by a Quanta reader that resembles Conway’s iconic Game of Life. Then we’ll enjoy a geometric puzzle that relates to some of his most visually pleasing work. First, we’ll play around with a numerical puzzle Conway invented that is perfection itself. ![]() This month, we celebrate the playful genius of the famous British mathematician with two puzzles and an exploratory game. He made original contributions to group theory (the Leech lattice, monstrous moonshine), higher-dimensional geometry, tessellations, knot theory, number theory ( surreal numbers), algebra, mathematical logic and analysis. He invented the “ Doomsday algorithm” (a fast method of calculating the day of the week in your head - Conway could do it in under two seconds) and countless games, including Sprouts and the famous Game of Life, which launched the study of cellular automata.Ī great deal of Conway’s serious mathematical work also arose from his penchant for playing mathematical games. He performed detailed analyses of many puzzles, such as the Soma cube, peg solitaire and Conway’s soldiers. The legendary mathematician John Horton Conway, who died in April of COVID-19, took a childlike delight in inventing puzzles and games.
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