Word Ways


Leslie E. Card


Among the nearly 70,000 ten-digit numbers representing the squres of 31, 501 to 99,381, inclusive, only 87 consist of unique digits, i.e., contain all ten digits 0 through 9. A list of these 87 squares is given by T. Charles Jones in the article "Squares with 9 and 10 Distinct Digits" published on pp. 62-63 of the Journal of Recreational Mathematics 1 (1968). Only 27 of these 87 numbers are the squares of five-digit numbers which likewise consist of unique digits.