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Even Digit Perfect Square(s) (Posted on 2008-10-25) Difficulty: 3 of 5
Determine all possible 7-digit decimal (base 10) perfect square(s), each of whose digits is nonzero and even.

Note: While a solution is trivial with the aid of a computer program, show how to derive it without one.

See The Solution Submitted by K Sengupta    
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Solution re: SLOANE A103705 (spoiler) | Comment 3 of 10 |
(In reply to SLOANE A103705 by Ady TZIDON)

1. Isn't it A030098? ... or A103751?

2. Now that a computer program is being used (IE, Firefox or Chrome), might as well do one tailored to the task instead:

DEFDBL A-Z
st = INT(SQR(1000000)): fin = INT(SQR(9999999))
FOR sr = st TO fin
 sq = sr * sr
 s$ = LTRIM$(STR$(sq))
 good = 1
 FOR i = 1 TO LEN(s$)
   IF INSTR("2468", MID$(s$, i, 1)) = 0 THEN good = 0: EXIT FOR
 NEXT
 IF good THEN PRINT s$
NEXT

2862864
8282884
8868484

I would be interested in how one could do this with no computer.


Edited on October 25, 2008, 5:10 pm

Edited on October 26, 2008, 1:56 am
  Posted by Charlie on 2008-10-25 17:05:34

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