Four 4-digit perfect squares are arranged one above the other, in ascending order. No two digits within any one of these squares is the same. If you sum the digits of each of these four squares, each result is the same sum. Also, the sum of the digits of each column formed by placing these digits above one another is the same. There may or may not be repeated digits within a column.
What are the 4-digit squares?
9801
5184
3249
1764 == each row and column adds to 18
Get squares from 1000 to 9801, then exclude any in which the same digit occurs more than once. Count the varieties of sums for the remaining -- only 18 and 19 occur four or more times (different squares). 19 can be easily excluded. Then test the 12 squares with digit sum of 18, in all combinations. The above is the only combination that works.
solution
