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The digits and square numbers (Posted on 2006-10-12) Difficulty: 3 of 5
All the nine digits are arranged here so as to form four square numbers.

9, 81, 324, 576

Which is the single smallest possible square number and a single largest possible square number using all the 9 digits exactly once?

What are the possible two, three & four number sets that follow this logic?

No Solution Yet Submitted by Salil    
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re: computer solution (spoiler) - Observation | Comment 2 of 3 |
(In reply to computer solution (spoiler) by Charlie)

The pan-digtal pairs of squares has some surprising features.

Among pairs with a one digit square there are five that use a 9 but none that use a 1 or a 4.  Why should there be such a difference in eight digit squares that don't repeat a digit?
(Charlie, maybe you could try excluding the other digits)

Among pairs with two digit squares, only 36 (two) and 81 (four) are represented.  Again, why not 16, 25, 49, 64?


  Posted by Jer on 2006-10-13 07:30:37
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