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Square Power (Posted on 2005-07-10) Difficulty: 4 of 5
I have put eight four-digit numbers together in a 4x4 grid, such that four can be read across and four downwards.

Four of my numbers are odd and four are even. I have one cubed number going across and one going down, and I have one fourth-power number going across and one going down. Two of the other numbers in the grid are squares.

Which two numbers in my grid are not perfect powers?

No Solution Yet Submitted by Sam    
Rating: 4.5000 (2 votes)

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Hints/Tips possible starts | Comment 2 of 7 |

These are the 11 possible fittings of fourth powers and cubes:

2744  9  4  1296  4096    46  6  4  2401  2401  2401  2401    46
4  0  2  0  3375  9  5    05  5  0  1000   0 3  70    8000    05
0  9  6859  3  6  1296  1296  6859  99    4913  4913   9 0  4096
1296  1296  1  1  3  1  9261  1296  76     6 1  46     6 0  9261

Six of these have a zero in the left column or top row, leaving 5:

9  4  1296    46  6  4    46
2  0  3375    05  5  0    05
6859  3  6  1296  6859  4096
1296  1  1  9261  1296  9261

What's left is to place one perfect square vertically and one horizontally.  I haven't been able to find such squares.

The program for the above:

CLS

DATA 1296,2401,4096,6561
FOR i = 1 TO 4: READ fourth$(i): NEXT

DIM cube$(12)
FOR i = 1 TO 12
  cube$(i) = LTRIM$(STR$(INT((i + 9) ^ 3 + .5)))
NEXT

FOR foNo = 1 TO 3
 FOR foNo2 = foNo + 1 TO 4
  FOR fRow = 1 TO 4
   FOR fCol = 1 TO 4
     IF MID$(fourth$(foNo), fCol, 1) = MID$(fourth$(foNo2), fRow, 1) THEN

FOR cNo = 1 TO 12
  FOR cNo2 = 1 TO 12
   IF cNo2 <> cNo THEN
     FOR cRow = 1 TO 4
      IF cRow <> fRow THEN
        FOR cCol = 1 TO 4
          IF cCol <> fCol THEN
           IF MID$(cube$(cNo), cCol, 1) = MID$(cube$(cNo2), cRow, 1) THEN
            IF MID$(cube$(cNo), fCol, 1) = MID$(fourth$(foNo2), cRow, 1) THEN
             IF MID$(fourth$(foNo), cCol, 1) = MID$(cube$(cNo2), fRow, 1) THEN
              REDIM grid$(4, 4)
              FOR i = 1 TO 4
               FOR j = 1 TO 4
                grid$(i, j) = " "
               NEXT
              NEXT
              FOR i = 1 TO 4
                grid$(fRow, i) = MID$(fourth$(foNo), i, 1)
                grid$(i, fCol) = MID$(fourth$(foNo2), i, 1)
                grid$(cRow, i) = MID$(cube$(cNo), i, 1)
                grid$(i, cCol) = MID$(cube$(cNo2), i, 1)
              NEXT
              flag = 1
              FOR i = 1 TO 4
                IF grid$(1, i) = "0" OR grid$(i, 1) = "0" THEN flag = 0
              NEXT
              IF flag THEN
                ct = ct + 1
                FOR row = 1 TO 4
                 FOR col = 1 TO 4
                  LOCATE row + 1, ct * 6 + col - 4
                  PRINT grid$(row, col);
                 NEXT
                NEXT
              END IF
             END IF
            END IF
           END IF
          END IF
        NEXT cCol
      END IF
     NEXT cRow
   END IF
  NEXT cNo2
NEXT cNo

     END IF
   NEXT fCol
  NEXT fRow
 NEXT foNo2
NEXT foNo

 


  Posted by Charlie on 2005-07-10 15:49:50
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