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?

The program opens with all 4 digit squares which have no repetion of digits as data.

It proceeds to compare squares with the same digital sum as well as comparing the sums of the 4 power positions.

Why Charlie specified ranking the squares in ascending order I have no idea but the concept greatly assisted in the writing of this program.

The program finds:
      Squares                    Row Sums   Column Sums
 1764  3249  5184  9801       18                 18

Copied from my spreadsheet:
                                     Row
N      N^2        Digits      Sum
42    1764    1   7   6   4   18
57    3249    3   2   4   9   18
72    5184    5   1   8   4   18
99    9801    9   8   0   1   18
  Col Sum  18  18  18  18



 CLS
 DATA 1024, 1089, 1296, 1369, 1764, 1849, 1936, 2304, 2401
 DATA 2601, 2704, 2809, 2916, 3025, 3249, 3481, 3721, 4096
 DATA 4356, 4761, 5041, 5184 ,5329, 5476, 6084, 6241, 6724
 DATA 7056, 7396, 7569, 7921, 8649, 9025, 9216, 9604, 9801

 DIM SHARED square(36)
 OPEN "sqinsq3.txt" FOR OUTPUT AS #1
 FOR a = 1 TO 36: READ square(a): NEXT

 FOR a = 1 TO 33
  FOR b = a + 1 TO 34
   FOR c = b + 1 TO 35
    FOR d = c + 1 TO 36

    p = square(a)
    q = square(b)
    r = square(c)
    s = square(d)
    v1 = INT(p / 1000)
    tmp = p - v1 * 1000
    v2 = INT(tmp / 100)
    tmp = tmp - v2 * 100
    v3 = INT(tmp / 10)
    tmp = tmp - v3 * 10
    v4 = tmp
    
    w1 = INT(q / 1000)
    tmp = q - w1 * 1000
    w2 = INT(tmp / 100)
    tmp = tmp - w2 * 100
    w3 = INT(tmp / 10)
    tmp = tmp - w3 * 10
    w4 = tmp
  
    x1 = INT(r / 1000)
    tmp = r - x1 * 1000
    x2 = INT(tmp / 100)
    tmp = tmp - x2 * 100
    x3 = INT(tmp / 10)
    tmp = tmp - x3 * 10
    x4 = tmp

    y1 = INT(s / 1000)
    tmp = s - y1 * 1000
    y2 = INT(tmp / 100)
    tmp = tmp - y2 * 100
    y3 = INT(tmp / 10)
    tmp = tmp - y3 * 10
    y4 = tmp

    tot1 = v1 + w1 + x1 + y1
    tot2 = v2 + w2 + x2 + y2
    tot3 = v3 + w3 + x3 + y3
    tot4 = v4 + w4 + x4 + y4

    row1 = v1 + v2 + v3 + v4
    row2 = w1 + w2 + w3 + w4
    row3 = x1 + x2 + x3 + x4
    row4 = y1 + y2 + y3 + y4

    tot5 = 0: row5 = 0
    IF (tot1 = tot2 AND tot2 = tot3 AND tot3 = tot4) THEN tot5 = 1
    IF (row1 = row2 AND row2 = row3 AND row3 = row4) THEN row5 = 1
    IF row5 = 1 AND tot5 = 1 THEN
    PRINT p; q; r; s, tot1; row1
    PRINT #1, p; q; r; s, tot1, row1
    END IF
 NEXT
 NEXT
 NEXT
 NEXT
 CLOSE 1

 

Posted by brianjn on 2009-08-31 21:47:29