MathDB

There are

n

holes in a circle. The holes are numbered

1,2,3

and so on to

n

. In the beginning, there is a peg in every hole except for hole

1

. A peg can jump in either direction over one adjacent peg to an empty hole immediately on the other side. After a peg moves, the peg it jumped over is removed. The puzzle will be solved if all pegs disappear except for one. For example, if

n=4

the puzzle can be solved in two jumps: peg

3

jumps peg

4

to hole

1

, then peg

2

jumps the peg in

1

to hole

4

. (See illustration below, in which black circles indicate pegs and white circles are holes.) http://i.imgur.com/4ggOa8m.png
[*]Can the puzzle be solved for

n=5

? [*]Can the puzzle be solved for

n=2014

?
In each part (a) and (b) either describe a sequence of moves to solve the puzzle or explain why it is impossible to solve the puzzle.

Problem Statement