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A Memory Problem (Brain Teaser)

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A Memory Problem

Q. Suresh Ratan was not too bad at remembering things but somehow he could never remember phone number even of his best friend Rajesh Sharad. He, therefore, jotted it down in his diary but unfortunately he misplaced the diary one day. Let us now try to help Suresh.

Delhi Telephones had opened some new centers recently. As a result of this, Rajesh’s telephone number had changed from six digits to seven digits. The exchange code had come to 3 digits from 2 digits. The first number of the code remained the same. The second number was now 1 less than the previous second number. And the third number was 1 if the last four figures of the previous phone number went to 5000 and if it was more than 5000, it would be 2.

It is significant to note that only the exchange code number had undergone a change in the revised phone number and that the last four digits remained the same. These last four digits of Rajesh’s phone form a complete square. When 4 is added to the new exchange code number, it becomes a complete square and the full phone number including the exchange code number also becomes a complete square and this is an astonishing aspect of this telephone number.

Now, will you work out the new and old phone numbers of Rajesh!

A. Rajesh Sharad’s old Phone No. 589604, new No. 5729604.