\(100,000\) buckets are lined up in a long row, numbered from \(1\) to \(100,000\).
The letters \(RITANGLE\) are dropped, in order and one at a time, into the buckets that are multiples of \(90\).
So \(R\) goes in bucket \(90\), \(I\) in bucket \(180\), and so on with \(E\) in bucket \(720\) and then starting again with \(R\) in bucket \(810\), and so on.
Similarly the letters \(TRIANGLE\) are dropped, in order and one at a time, into the buckets that are labelled with the triangular numbers.
So \(T\) goes in bucket \(1\), \(R\) in bucket \(3\), and so on with \(E\) in bucket \(36\) and then starting again with \(T\) in bucket \(45\), and so on.
What is the number of the first bucket that receives two copies of the same letter?
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