Question :
A little girl counts from 1 to 1000 using the fingers of her left hand as follows. She starts by calling her thumb 1, the first finger 2, middle finger 3, ring finger 4, and little finger 5. Then she reverses direction, calling the ring finger 6, middle finger 7, the first finger 8, and her thumb 9, after which she calls her first finger 10, and so on. If she continues to count in this manner, on which finger will she stop?
Solution :
She will stop on her first finger.
Here is how the finger count starts:
It is easy to see that the counting falls on the same finger every eighth number called. Therefore to answer the question, all one needs is to find the remainder of the division of 1000 by 8, which is equal to 0. This implies that when the girl reaches 1000, she will be on her first finger (moving from the middle finger), the same one she will be on while calling any number divisible by 8.
