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Find this cube! (Posted on 2012-06-16) Difficulty: 3 of 5
What is the smallest palindrome that is the cube of a non-palindromic number?

See The Solution Submitted by Ady TZIDON    
Rating: 4.2000 (5 votes)

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Solution 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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