Reflection Maze
By Scott Kim, April 19, 2011, for the Wall Street Journal
Instructions. Every square in this maze contains a letter P. You may jump from one
square to another square in the same row, column or diagonal only if you can draw
a mirror line so that one P is the exact reflection of the other P. Or to put it another
way, you must be able to fold the paper so that one P exactly coincides with the
other P.
Example moves. For instance you can jump from the Start square to any of the
three dark squares below, by reflecting the first P about one of the three dotted
lines. Note that some of the mirror lines are diagonal. Diagonal reflections can be
hard to understand, since tilted mirrors are unusual. To verify whether two P’s are
reflections of each other about a diagonal mirror line, first turn the paper so the
mirror line is vertical.
Shown below are examples of illegal moves. From the start square, you cannot jump
to square 1 because it is not in the same row, column or diagonal. You cannot jump
from Start to square 2 because there is no line that reflects one P into the other P.
Similarly, you cannot jump from Start to square 3, because the two P’s are not
reflections of each other.
Challenges
1. [easy] Look at the reflection maze above. From which squares can you jump to the
End square?
2. [medium] Get from Start to End by jumping from square to square. There are
many solutions; find a solution with the fewest jumps.
3. [hard] Find a second path from Start to End that uses completely different
squares from the solution to challenge 2, except of course for the Start and End
squares. Again, find a solution with the fewest jumps.
4. [very hard] Find a path from Start to End that visits every square just once. Hint:
identify the squares from which you can jump to only two other squares. The
answer is unique.
ANSWERS
1. There are two squares you can jump from to get to the End square, shown below.
2. The shortest solution has 5 jumps, as shown below.
3. Here is a second solution, again with 5 jumps, that visits completely different
squares.
4. Here is the only path from Start to End that visits every square just once.