==> competition/games/think.and.jump.s <==
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