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 Square Power (Posted on 2005-07-10)
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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 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    464  0  2  0  3375  9  5    05  5  0  1000   0 3  70    8000    050  9  6859  3  6  1296  1296  6859  99    4913  4913   9 0  40961296  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    462  0  3375    05  5  0    056859  3  6  1296  6859  40961296  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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