THINK & JUMP: FIRST THINK, THEN JUMP UNTIL YOU ARE LEFT WITH ONE PEG!

competition/games/think.and.jump

Problem

THINK & JUMP:  FIRST THINK, THEN JUMP UNTIL YOU
               ARE LEFT WITH ONE PEG!                      O - O   O - O
                                                          / \ / \ / \ / \
                                                         O---O---O---O---O
BOARD DESCRIPTION:  To the right is a model of            \ / \ / \ / \ /
                    the Think & Jump board.  The       O---O---O---O---O---O
                    O's represent holes which         / \ / \ / \ / \ / \ / \
                    contain pegs.                    O---O---O---O---O---O---O
                                                      \ / \ / \ / \ / \ / \ /
                                                       O---O---O---O---O---O
DIRECTIONS:  To play this brain teaser, you begin         / \ / \ / \ / \
             by removing the center peg.  Then,          O---O---O---O---O
             moving any direction in the grid,            \ / \ / \ / \  /
             jump over one peg at a time,                  O - O   O - O
             removing the jumped peg - until only
             one peg is left.  It's harder then it looks. 
             But it's more fun than you can imagine.

SKILL CHART:

        10 pegs left - getting better
         5 pegs left - true talent
         1 peg  left - you're a genius

Manufactured by Pressman Toy Corporation, NY, NY.

Show solution

Three-color the board in the obvious way.  The initial configuration has 12
of each color, and each jump changes the parity of all three colors.  Thus,
it is impossible to achieve any position where the colors do not have the
same parity; in particular, (1,0,0).

If you remove the requirement that the initially-empty cell must be at the
center, the game becomes solvable.  The demonstration is left as an exercise.

Karl Heuer   rutgers!harvard!ima!haddock!karl   karl@haddock.ima.isc.com




Here is one way of reducing Think & Jump to two pegs.


Long simplifies Balsley's scintillating snowflake solution:

1  U-S           A - B   C - D
2  H-U          / \ / \ / \ / \
3  V-T         E---F---G---H---I
4  S-H          \ / \ / \ / \ /
5  D-M       J---K---L---M---N---O
6  F-S      / \ / \ / \ / \ / \ / \
7  Q-F     P---Q---R---S---T---U---V
8  A-L      \ / \ / \ / \ / \ / \ /
9  S-Q       W---X---Y---Z---a---b
10 P-R          / \ / \ / \ / \
11 Z-N         c---d---e---f---g
12 Y-K          \ / \ / \ / \ /
13 h-Y           h - i   j - k
14 k-Z

The board should now be in the snowflake pattern, i.e. look like

         o - *   * - o
        / \ / \ / \ / \
       *---o---*---o---*
        \ / \ / \ / \ /
     *---*---*---*---*---*
    / \ / \ / \ / \ / \ / \
   o---o---o---o---o---o---o
    \ / \ / \ / \ / \ / \ /
     *---*---*---*---*---*
        / \ / \ / \ / \
       *---o---*---o---*
        \ / \ / \ / \ /
         o - *   * - o

where o is empty and * is a peg.  The top and bottom can now be reduced
to single pegs individually.  For example, we could continue

15 g-T
16 Y-a
17 i-Z
18 T-e
19 j-Y
20 b-Z
21 c-R
22 Z-X
23 W-Y
24 R-e

which finishes the bottom.  The top can be done in a similar manner.
-- 
Chris Long