The Repunit Factor

11 x 111 = 1,221, and 11 x 1,111 = 12,221. See the pattern? Multiplying 11 by a repunit (a number made of all 1s) produces a palindrome that reads the same in both directions. The idea extends further: 111 x 111 = 12,321, a tidy numerical pyramid that climbs and descends.

For three-digit numbers, the same idea extends one step. Each interior digit becomes the sum of its two neighbors in the original number. For 11 x 234: keep the outer digits 2 and 4, then fill the gaps with 2+3=5 and 3+4=7, giving 2,574. If any of those sums passes 9, carry into the digit on its left, exactly like the two-digit case.