RU-ALLRUSSIAN 1977 Problem 10

We call a number doubly square if (1) it is a square with an even number 2n of (decimal) digits, (2) its first n digits form a square, (3) its last n digits form a non- zero square. For example, 1681 is doubly square, but 2500 is not. (1) find all 2- digit and 4- digit doubly square numbers. (2) Is there a 6- digit doubly square number? (3) Show that there is a 20- digit doubly square number. (4) Show that there are at least ten 100- digit doubly square numbers. (5) Show that there is a 30- digit doubly square number.