Joe's latest puzzle for Penny consists of nine consecutively numbered pegs and a disc with 10 holes. The disc is free to rotate about its center.

The top position of the circle at any given time is marked by a fixed arrow pointer. A peg may be inserted in the disc in an empty hole adjacent to the arrow. If that hole isn't empty, she can't continue placing pegs.

The pegs are numbered, and after each one is placed, the disc is rotated that many positions clockwise. Penny has succeeded in placing all the pegs in the holes on the disc and has left an empty spot at the top adjacent to the arrow pointer, as shown in the following diagram. I've marked the empty spot that remains, with a hyphen:

                 |
                 V

                 -

       1                   9



 z                               x





 7                               2



       3                   8

                 y
                 

But Penny doesn't remember in which of the positions marked x, y and z were the 4, 5 and 6 at the end of the game.

In what order did Penny place the pegs?

Okay, I can't seem to figure out whether this is what you want or not. When you say "adjacent to the arrow", do you mean the hole the arrow is pointing to? Because if so, the solution is too simple. If you mean one of the two holes next to the one the arrow is pointing to, then "If that hole isn't empty..." makes no sense.

For the record, if the meaning is the hole the arrow is pointing to, the answer is:
6, 1, 4, 8, 3, 2, 9, 5, 7

Looking at the problem again, this solution seems to be right. But it's too easy, no? Am I missing something again?

Edited on January 17, 2007, 6:41 pm

Posted by TamTam on 2007-01-17 15:01:23