Are you really going to count to 2015?

Number Theory Level 3

One day, Mr Tan tested his five children, "Suppose I count from 1 to 2015 on my left hand's fingers. I begin on my thumb and work my way to my little finger and back to my thumb again (without skipping a finger) and just keep repeating this. On which finger will I count 2015?"

The answers given by his children were:

  • Charles: "Thumb."

  • Darius: "Index finger."

  • Brenda: "Middle finger."

  • Alfred: "Ring finger."

  • Eric: "Little finger."

Details and assumptions:

  • Mr Tan has five fingers on a hand like anyone else haha.

  • Mr Tan counts exactly one number for each finger.

  • Whenever Mr Tan reaches his thumb or little finger, he counts only one number there, after which he reverses direction.

Yes, one of the five siblings MUST be correct. But which one???


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