"RATS! I Have No Clue."
Your friend Sam gives you this sequence.
"What is the next term?" he asks.
"I will say that the next term is , because the value of ," you reply.
"Yes, that is one answer," Sam concedes. "But what if I told you that the sequence is
"What, then, is the next term?"
The answer is 145.
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1 solution
A hint lies in the title: RATS actually stands for R everse, A dd, T hen S ort. We obtain this procedure:
1 : Reverse the digits of the term (i.e. 1 0 a + b becomes 1 0 b + a ). If the term is a single digit, then skip this step.
2 : Add the term and the transformed term together (i.e. ( 1 0 a + b ) + ( 1 0 b + a ) = 1 0 ( a + b ) + ( a + b ) ). You may recognize this as an iterative algorithm for obtaining palindromes.
3 : Sort the digits from least to greatest, and write them down, from left to right (i.e. 1 6 5 = 1 0 0 ( 1 ) + 1 0 ( 6 ) + 1 ( 5 ) ; 1 < 5 < 6 ; 1 6 5 → 1 5 6 ).