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 Find this cube! (Posted on 2012-06-16)
What is the smallest palindrome that is the cube of a non-palindromic number?

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 computer solution | Comment 2 of 4 |

DEFDBL A-Z
FOR i = 1 TO 99999
cube = i * i * i
cs\$ = LTRIM\$(STR\$(cube))
pal = 1
FOR j = 1 TO LEN(cs\$) / 2
IF MID\$(cs\$, j, 1) <> MID\$(cs\$, LEN(cs\$) + 1 - j, 1) THEN pal = 0: EXIT FOR
NEXT
IF pal THEN PRINT cube; TAB(18); i
NEXT

finds

` 1                1 8                2 343              7 1331             11 1030301          101 1367631          111 1003003001       1001 10662526601      2201 1000300030001    10001 1030607060301    10101 1334996994331    11011 `

showing the first 11 palindromic cubes together with their cube roots. Only 10662526601 has a non-palindromic cube root: 2201.

To get to larger cubes without worrying about accuracy, we go to UBASIC:

10     for I=1 to 9999999
20       Cube=I*I*I
30       Cs\$=cutspc(str(Cube))
40       Pal=1
50       for J=1 to int(len(Cs\$)/2)
60         if mid(Cs\$,J,1)<>mid(Cs\$,len(Cs\$)+1-J,1) then Pal=0
70       next
80       if Pal then print Cube;tab(28);I
90     next

finds

` 1                           1 8                           2 343                         7 1331                        11 1030301                     101 1367631                     111 1003003001                  1001 10662526601                 2201 1000300030001               10001 1030607060301               10101 1334996994331               11011 1000030000300001            100001 1033394994933301            101101 1331399339931331            110011 1000003000003000001         1000001 1003006007006003001         1001001 1331039930399301331         1100011 `

showing that even if we go to 19-position cubes, there is still only one palindromic cube of a non-palindromic number.

 Posted by Charlie on 2012-06-16 12:56:15

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