![]() In addition, University of Colorado mathematician Alexander Soifer told Quanta Magazinethat the duo didn’t just want to brute-force the problem, but wanted to “solve it in an impressive way. So, even with the “don’t worry about symmetrical results” rule in place, the computation to test 14 was going to take too long for the satisfaction of Subercaseaux and Heule. So, they implemented the “don’t worry about symmetrical results” rule and were able to rule out 13, leaving just 14 and 15 on the table.īut every time the number tested got bigger, the computer process took a whole lot longer. Mirroring the whole grid wouldn’t change the result, but it would double the amount of work the computer had to do. They figured out that, for the sake of this problem, symmetrical answers are the same. Unfortunately, that takes a lot of time to do, even for a highly advanced and extremely powerful computer. Especially because, in order to rule out a potential answer, they had to make sure they tried every single combination of number placements. But that group of answers had already been achieved by another team a few years before, and Subercaseaux and Heule wanted a true answer, not a range of possibilities. After all, the problem took top mathematicians over a decade to solve, and it wasn’t possible without a lot of computing power and a fair amount of creativity.Īccording to a Quanta Magazine article, the duo who solved the problem- CMU grad student Bernardo Subercaseaux and CMU professor Marijn Heule-originally managed to narrow the list of potential answers down to just 13, 14, or 15. Their “taxicab distance” from their nearest repeat had to be one more than their value. The same rule goes for all the other numbers. But they could be diagonal from each other, because their “taxicab distance” would be two-one to the side and one up or down. So, for example, two 1s could not be right next to each other, because their “taxicab distance” would only be one square. The question, originally posed in 2008, went as such: If you had an infinite grid of squares-like a sheet of graph paper that went on for eternity-and you wanted to fill it with numbers that had to be more-than-that-number squares apart, what is the minimum number of different numbers you would need? This is called the “packing coloring” problem.Īnd it had this caveat-repeating numbers’ distance “apart” refers to something called their “taxicab distance,” meaning you only squares between numbers in straight lines along paths made of right angles. Usually, big, complicated math problems that are hard to solve have big, complicated answers that are almost equally hard for the layperson to understand. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. Adding to 10: Ariel was playing basketball. They found an answer to how many numbers you need to fill an infinite grid under specific conditions.ġ5: That’s the answer to an incredibly complicated math problem recently solved by a two-person team at Carnegie Mellon University (CMU). 120 Math word problems, categorized by skill Addition word problems Best for: 1st grade, 2nd grade 1.A duo of mathematicians just solved a 15-year-old problem.
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