What is the remaining letter?
The word was written times to form a long string First, all letters in the odd places of the string were erased. Then, in the string obtained, once again all the letters in the odd places were erased, and so on. At the end of these operations, only one letter remained. What is this letter?
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1 solution
Number the sequence from 1 to 9 0 0 . each time the operation is applied, odd numbers are dismissed and even numbers get halved. A letter would be dismissed, in exactly n + 1 steps, if its initial associated number is of form a × 2 n , where a is an odd number. We just need to find a number between 1 and 9 0 0 (inclusive) that has the highest power of 2 , as its factor. That number would be 5 1 2 . its associated letter is "N".