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Australian AMC 2013 - Intermediate Question 11

AMC AUSTRALIA · Australian AMC 2013 - Intermediate

Question 11

Start with the number 1 and create the sequence

$$1,2,4,8,16,22,24,28,\ldots$$

where each number is the sum of the previous number and its final digit. How many numbers in the sequence are less than 1000?
  1. 10
  2. 100
  3. 101
  4. 200
  5. 201