111,111,111 x 111,111,111 = 12,345,678,987,654,321

The story behind the answer

True. Write 111,111,111 as 10^0 + 10^1 + … + 10^8. When you square it, you add products 10^i × 10^j = 10^{i+j}. For each total exponent k, the number of pairs (i, j) with i + j = k forms the triangular sequence 1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1. The largest coefficient is 9, so there are no carries, and the digits appear exactly as 12,345,678,987,654,321.

Numbers made of all 1s are called repunits. In base 10, squaring n ones (with n ≤ 9) always yields the palindrome 123…n…321. Mnemonic: “Ones squared build a pyramid of digits—climb to n, then back down.”