how many sheep?

Question

Sneaking Up the Line Eric the sheep is at the end of a line of sheep waiting to be shorn. But being an impatient sort of a sheep, every time the shearer takes a sheep from the front to be shorn, Eric sneaks up the line two places. If there are 49 sheep ahead of him, how many of the sheep will be shorn before Eric?

Answer 1

The sheep in position number 1 gets shorn.

 

Eric starts at position 50 ("49 sheep ahead of him"). When a sheep gets shorn (that's 1 less), Eric moves up 2 positions (that's another 2 less), so:

   number of sheep shorn       Eric's new position

              0                                  50             [start]

              1                                  47

              2                                  44

              3                                  41

              4                                  38

              5                                  35

              6                                  32

              7                                  29

              8                                  26

              9                                  23

             10                                 20

             11                                 17

             12                                 14

             13                                 11

             14                                   8

             15                                   5

             16                                   2

             17                                   1  (can't move up this time)

        Eric's turn

 

   Eric is now in position 1 in the queue and gets "served" (a queuing theory term).

 

   17 sheep are shorn before Eric.

      [note:  Now, if you want a shortcut, divide 50/3 = 16 2/3, but always round up.]

Answer 2

For each shearing the line diminishes by 3 sheep - one is shorn and Eric skips 2.

 

49 - n(3) = 0

49 - 3n = 0

49 = 3n

16 1/3 = n

 

After 16 sheep get shorn Eric is at the head of the line.