The Amazing Pattern When Multiplying 111,111,111

Discover the fascinating pattern when you multiply 111,111,111 by itself. Explore the remarkable result and see how this number trick reveals a beautiful symmetry! If we multiply nine ones in a row by nine ones (in other words, if we raise the number 111,111,111 to the power of two), we get a very remarkable result. Can you guess it quickly?

A small hint: if you first try 11 × 11 = 11² = 121, then 111 × 111 = 111² = 12321, everything might become clear to you. The result of the square of nine ones in a row (or the number 111 million 111 thousand 111), gives—perhaps not surprising—but a very remarkable and aesthetic result:

111,111,111 × 111,111,111 = 111,111,111² = 12,345,678,987,654,321.

So we nicely climb from one to nine and then descend back to one. By the way, could you correctly read such a large resulting number? The answer is: 12 quadrillion 345 trillion 678 billion 987 million 654 thousand 321.

Why did it turn out this way? Just remember manual multiplication of numbers in elementary school:

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Based on the original Czech article: Hra s čísly: kolik je 111 111 111 × 111 111 111?.