Problem 98

Problem 98

Anagramic squares

By replacing each of the letters in the word CARE with 1, 2, 9, and 6 respectively, we form a square number: 1296 = 362. What is remarkable is that, by using the same digital substitutions, the anagram, RACE, also forms a square number: 9216 = 962. We shall call CARE (and RACE) a square anagram word pair and specify further that leading zeroes are not permitted, neither may a different letter have the same digital value as another letter.

Using words.txt (right click and ‘Save Link/Target As…’), a 16K text file containing nearly two-thousand common English words, find all the square anagram word pairs (a palindromic word is NOT considered to be an anagram of itself).

What is the largest square number formed by any member of such a pair?

NOTE: All anagrams formed must be contained in the given text file.


将单词CARE中的四个字母依次赋值为1、2、9、6,我们得到了一个平方数:1296 = 362。神奇的是,使用同样的数字赋值,重排后的单词RACE同样构成了一个平方数:9216 = 962。我们称CARE和RACE为重排平方单词对,同时规定这样的单词对不允许有前导零或是不同的字母赋相同的值。