Ramaiah's classes were (are) popular coaching classes for IIT JEE exam preparation in Hyderabad. They themselves had an entrance exam!
These Ramaiah entrance tests contained some very nice problems.
This was a question I first saw on a Ramaiah entrance test when my brother appeared for it (1990). The question is actually much older than that, probably the 1800s.
Anyway, here goes:
Consider the sequence of numbers
$$49, 4489, 444889, \dots $$
Each number is formed by inserting 48 in the middle of the previous number.
$$49 \to 4\underline{48}9 \to 44\underline{48}89 \to \dots$$
Show that all these numbers are perfect squares!
[Solution]
These Ramaiah entrance tests contained some very nice problems.
This was a question I first saw on a Ramaiah entrance test when my brother appeared for it (1990). The question is actually much older than that, probably the 1800s.
Anyway, here goes:
Consider the sequence of numbers
$$49, 4489, 444889, \dots $$
Each number is formed by inserting 48 in the middle of the previous number.
$$49 \to 4\underline{48}9 \to 44\underline{48}89 \to \dots$$
Show that all these numbers are perfect squares!
[Solution]
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