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?

Edited on July 16, 2023, 2:52 am

Edited on July 16, 2023, 2:53 am

Posted by K Sengupta on 2023-07-16 02:52:13