Enigma 1504 - All ten digits

Enigma 1504 - All ten digits
New Scientist magazine, 26 July 2008.
By Richard England.

Harry has chosen some 5-digit perfect
squares (all different) which use only the
digits 0 to 4, none of them starting or
finishing with the digit 0. Each of the
digits 0 to 4 is used a different number of
times in his squares, those numbers of times
being 5 to 9.

(1) Which eligible square or squares has
Harry NOT chosen?

Tom has chosen some 5-digit perfect squares
which only use the digits 5 to 9. Each of
the digits 5 to 9 is used a different number
of times in his squares, those numbers of
times being 0 to 4.

(2) Which squares has Tom chosen?

Ciao,
Chappy.
.

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