The 11th World Puzzle Championship
Article for Spring 2001 Games World of Puzzles
Selected Puzzles from the 9th WPC
Published in the World Puzzle Federation Newsletter
WPC Puzzle Page
The organizers of the 9th WPC thank the
puzzle and game manufacturers who donated their products for use during the WPC.
||Binary Arts -
||Hasbro and Wizards of the Coast -
Mr. Potato Head, DragonStrike, Magic: The Gathering
||Zometool - Zome
This year's competition was highlighted by an
unprecedented variety of puzzles on paper. Of course, this is the direct result
of the ingenuity of the puzzle designers. Thanks go to all who contributed.
Of particular note is the extraordinary support from
Erich Friedman, who contributed 18 separate puzzle designs. This includes the
Multi-Level Rolling Block Maze featured in Part III, and 10 of the 13 Battleship
puzzles presented in Part V. Thank you, Erich!
(IV.2), Chasm Maze (VII.13)
Track(I.18), Gridlock(I.19), Weighted Battleships (V.9), Stepping Stones
(I.7), Rectangles (I.12), Tents (I.14), Spokes (VIII.7), Black&White
(VIII.8), Eminent Domain (VIII.10), Lay Bricks (VIII.12), Fences
(I.6), Crossword Maze (VII.2)
(I.9), Balancing Act (I.10), Rolling Block Maze (I.15), Multi-Level
Rolling Block Maze (III), Non-rounded Battleships (V.2), Squared
Battleships (V.3), Minesweeper Battleships (V.5), Ship Battleships
(V.6), Easy as Battleships (V.7), Crowded Battleships (V.8), Retrograde
Battleships (V.10), Either/Or Battleships (V.11), Diagonal Battleships
(V.12), Hexagonal Battleships (V.13), Numerical Jigsaw (VIII.1), Do or
Die (VIII.9), Equations (VIII.14), Hexasperation (VIII.19)
Head (VI.1), Hawaiian Holiday (VI.7), Playground (VI.8), Block Party
(VI.4), Work Product (VI.5)
Corners (I.3), Symbolic Dominoes (I.20), End View (VIII.2), RecTangles
(VIII.4), Number Place (VIII.17)
Test (VI.9), Olympic Spirit (VI.10)
(I.5), Overlay (I.8), Lunar Lockout (II.1,2,4), Zome K6 (IV.4), Connect-i-cut
(VII.3), Board Stiff (IX.1), Triangle Count (IX.2), CONN Tour (IX.3),
Vantage Point (IX.7), Cube Patterns (IX.8)
|Cut the Q
Balance (VI.2), Dungeon Escape (VI.3)
(VII.1), Viewpoint (VIII.5; IX.6)
Pyramid (IV.1), Tangram Battleships (V.4)
|3-D Paint by
Study (VI.11), Hidden Puzzle (VI.13)
(I.2), River Crossing (I.11), Next! (VIII.3), Gold Medal Boggle
(VIII.11), Cartoon Sequence (IX.5)
The 9th World Puzzle Championship--Back in
Article for Spring 2001 Games World of Puzzles
The 9th World Puzzle Championship
returned to the United States for the first time since its inception in
1992. And what a homecoming it was. The host US team was hospitable in
every way, except when it came to dispatching the competition--running
away with the team title for the third year in a row.
After two days of renewing old
friendships, making new acquaintances, and sightseeing in New York City,
the contestants settled down and got to the business at hand: solving
puzzles! After two long, grueling days of competition, 4-time champion
and favorite Wei-Hwa Huang gained an impressive lead over the rest of
the field. However, it's never over until it's over; and this year,
organizers added a final playoff round to put an exclamation mark on the
The top 10 individuals going into the
final playoff round were handicapped based on their point score. 10th
place received 30 minutes to solve the 8 problems, with 1st through 9th
receiving proportionately more time, based on the points earned during
the previous rounds. Aside from the time handicap, the scores from the
previous rounds were ignored in determining the rank of the top 10
Despite an intimidating 11 minute head
start on the rest of the field, Wei-Hwa Huang made one miscalculation
that he did not notice and correct until just 2 minutes remaining in the
round. This opened the door for German Ulrich Voigt, who calmly ignored
his 15 minute disadvantage and solved each problem correctly, finishing
his last problem with just over 4 minutes remaining in the round. The 2
minutes, 11 second difference made Ulrich the first new champion in 4
Also among the top 10 finalists were US
team members Zack Butler (6th) and Ron Osher (9th), and Canadian Derek
The competition events concluded with a
museum exhibit of jigsaw and mechanical puzzles hosted by puzzle experts
Anne D. Williams and Jerry Slocum, and a festive awards dinner at the
home of US Team member Ron Osher.
The following pages contain some of our
favorite puzzles from the competition, designed by some of the best
puzzle and game designers from around the country. We hope you enjoy
their puzzles as much as we have. We would also like to acknowledge the
companies that donated products used during the competition: Binary
Arts, Wizards of the Coast/Hasbro, and Zometool; our online host:
PuzzleTime.com, and longtime sponsor: Random House.
The 10th World Puzzle Competition will be
in the Czech Republic later this year. Open qualifying to select some
members of the US and Canadian teams will be held on Saturday, June 9.
Visit the US Team web site at www/puzzles-usa.org for details.
- Nick Baxter and Will Shortz
Selected Puzzles from the 9th WPC
Published in the World Puzzle Federation Newsletter
like to present an overview of the puzzles used from the 9th World
Puzzle Championship last year, highlighting those that I think are the most
interesting. Actually, I think ALL the puzzles were interesting in some way or
another, otherwise I would not have included them in the competition! So please
don't be too disappointed if I did not include your favorites here.
Part I, we tried to lighten up the first round of competition with a
little bit of fun. Since the first day was Friday the 13th, this was
an obvious theme to use for a few of the puzzles. The most obvious example was
the very first puzzle: a word-search using the names of movie stars appearing in
the Friday the 13th horror film series. (since the movies were
so bad, these actors and actresses have never been heard from again, so the
rules of culture-neutrality didn't apply!)
puzzle is a little scarier than the normal word search: we've left out one of
the 36 first and last names, and ask you to
figure out which one is missing!
grids" have become a staple of the WPC, and a number of styles have become
recurring favorites. So it's always refreshing to see a new, innovative style
appear, which sums up my enthusiasm for the Railroad Track puzzle.
Lay a single, closed loop of railroad track that travels
through every square of the grid. The track connects squares horizontally or
vertically, and crosses itself only in the squares with crosses. (All the
crossing are already placed.)
The track does not turn as it passes through the stations,
which are the squares containing numbers. As you follow the track, visit
stations 1 through 13 in order, then return to station 1.
Instruction Booklet and the pre-competition rules meetings are important parts
of keeping the competition fair for everyone. The authors and editor must strike
a delicate balance between giving enough information ahead of time so the that
puzzles will be readily understood, and not giving too much
information so that the puzzle could be solved ahead of time.
a case where we gave away too much information. The puzzle was actually a
two-part puzzle in disguise. The first part was to determine the set of
dominoes; only then could you begin to solve the second part and actually locate
them in the grid. Of course, my hope was that people would have to discover the
unique set of dominoes during the competition. But unfortunately, this challenge
became obvious during rules meeting, and I think that most smart solvers
discovered the tricks the night before.
nothing else, I recommend that you at least determine the complete configuration
of the unusual set of dominoes in the problem below.
A set of 28 dominoes is in an 8x7
rectangular tray. The layout is shown but without the domino edges. Reconstruct
the missing edges.
This unusual set of dominoes uses 3 symbols
(circle, arrow, and double-arrow) and their orthogonal rotations. All
permutations of the symbols are included in the set, except that duplicate
patterns due to rotational symmetry are excluded. For example, dominoes A and B
are the same, but A and C are different.
II was a
speed round featuring the Lunar Lockout game. The US Team first saw this
puzzle type (then known as UFO) in the 1999 U.S. & Canadian team
qualifying test, and then again during the 2000 qualifier. It was originally
designed by Nob Yoshigahara as a paper puzzle, but Binary Arts quickly saw the
commercial potential, and eventually produced the game. They were also generous
enough to give the game to each of the competitors so that all solving could be
the with physical model rather than on paper (which is a LOT harder to do--just
ask the US team!)
puzzles appear to be easy, but they are not. I like to describe them as a maze
where the barriers move along with your pieces, but the complexity is
surprisingly more profound than that.
section originally wasn't a timed event, and included one additional puzzle.
Mercifully, we changed our minds, and removed the hardest (and most unique) of
the puzzles. So that no one is deprived of the experience, I include it here.
The goal is to end up with the red robot on the center space
within the specified number of moves. Unfortunately in this puzzle, the red
robot is invisible. You must locate the only starting position for the
red robot so that a solution is possible, and then discover the 7-move solution.
Each robot travels horizontally or vertically, but only
directly toward another robot--as far as it can go until hitting it edge to
edge. One move is a continuous sequence of such traverses made by the same
I would not do justice to the physical and manipulative puzzles used in Part
III and Part IV if I reproduced them here. So I won't try. These sections included a representative cross section of popular styles
(sliding block, maze, edge-matching, 2D tray, and 3D geometric assembly), and
were carefully designed and selected to reward deduction, not trial-and-error or
luck. The typical WPC participant is not as experienced with these types of
puzzles, so the scores were down, particularly for Part IV. Regardless, I hope
that future WPC organizers share my view of the importance of these puzzle
styles, and will continue to include manipulative puzzles in the competition.
really like puzzles that combine different themes together into a good new
design. The Battleship style is ripe for this, as we saw in Budapest with Battleship
Varia. For Part V, we continued this theme by using Erich Friedman's
large collection of new variations.
the big surprise for me was Serhiy Grabarchuk's Tangram Battleship -- a
beautiful combination of the classic manipulative puzzle design and one of the
WPC's all-time favorite puzzle styles. The triangular shapes are very unusual,
making the puzzle a little more difficult because the solver must be very
careful to make sure that ships don't touch at a single point (and at the same
time must remember to take advantage of this restriction!).
Locate the position of the 7-ship fleet in the grid. The fleet
is shown to the right of the grid: one ship for each of the seven classic
Tangram shapes. The ships are divided into identical isosceles right
triangular segments. Ships can be rotated and reflected, and do not touch
each other, not even at a single point.
The numbers around the edges of the grid reveal the total
number of triangular ship segments that appear in the respective column
VI revived a
theme we saw in Utrecht at the 5th WPC--puzzles that required a bit more time to
solve, and rewarded inspired thinking rather than just brute force or speed.
This is another class of puzzles that I think is valuable, and I hope is used
again in future competitions.
couldn't have been happier with the set of puzzles created by the R&D team
at Wizards of the Coast; each of them are worthy of being presented here!
However one stands out as being particularly innovative. Balloon Balance
was designed by Richard Garfield, the original inventor of the Magic: The
Gathering card game. He took the classic balancing puzzle and then removed
gravity! Well, almost. What he did do was to remove the top-level fulcrum, and
thus remove the orientation of the force of gravity. He then added helium
balloons in addition to normal weights, so that some objects pulled up while
some pulled down. Once you ignore what seems to be missing and orient yourself
properly, it's not as hard as it first seems.
|Add the weights and balloons to the diagram so that the
entire mechanism is in equilibrium. As with normal balance puzzles, the total
torque at each fulcrum must be zero.
puzzles, rewarding intuitive solving skills, have appeared in a few recent
championships, and I felt this style was worthy of being included again this
year as Part VII. However, the original version of Scott Kim's Triangles
would have been more a question of accurate counting (and also a disaster for
judging), so I decided to limit the search to just equilateral triangles rather
than triangles of any shape.
few of the behind-the-scenes events will further illustrate how awkward this
sort of problem can be. Scott's original solution diagram reportedly gave 109
triangles. When testing the original version, I ignored the original solution,
finding a better diagram with 123 triangles. This is when I changed the goal and
returned the original problem back to Scott for publication in one of his
magazine articles. When rechecking the count for this article, I could only get
121; Scott's editors had the same trouble. Wei-Hwa Huang was nice enough to
confirm the lower count, but also found a better solution with 127 triangles.
Ironically, his new diagram was the same as Scott's original, just with a more
accurate count! Upon seeing this result, I tweaked it slightly to improve the
maximum even higher.
Here is the original version of the problem.
Test your reasoning and intuition skills (if not your counting!), and think
about what is most likely to increase the triangle count:
What are the best points around the
outside of the large triangle (vertices, mid-points, quarter-points, other?)
through which the new lines should pass?
Should the new lines go through the
three interior intersection points or maximize the number of interior lines
that are crossed?
Should the new lines cross each other
inside, outside, or on the edge of the large triangle?
How does the count change as you adjust
the new lines to slightly different positions?
And how do you balance the benefits of these
|In the diagram below, there are 27 triangles of various
sizes, shapes and orientations. Add three lines (of any length) anywhere in the
diagram so that the total number of triangles (of any size, shape or
orientation) is maximized.
last round, Part VIII, was another mix of various puzzle types, and
included many familiar WPC puzzle styles. Viewpoint is Scott Kim's twist
on the classic idea of 3D cube visualization. The original design included
16 figures, but I decided to simplify the puzzle by only using half; we then
used the remaining eight figures for the Viewpoint 2 puzzle that appeared
in the final round! It turned out well, with each of the separate sets being an
Each of the 8 blocks shown is composed of 6 identical
cubes. (The perspective of the drawing sometimes hides some of the rear cubes.
Figuring out their position is part of the puzzle.) Group the 8 blocks into 4
pairs of identical shapes.
puzzles used for Part IX, the playoff round, were selected because they
were visually appealing, required less than the normal amount of paper work to
solve, and still presented a moderate challenge to the finalists. The surprise
of the round was definitely the unassuming Triangle counting
problem--only 2 of the 10 finalist got this one right, and it was the deciding
factor for the individual title. Before you read on, you might take some time
now and try solving it for yourself.
How many triangles (of any shape) are in the figure?
are a number of ways to tackle a problem like this; most are equally valid, but
some are significantly more reliable than others. The most typical approach for
this type of problem is to determine all the possible triangle shapes, and then
determine how many of each type there are. The symmetry of this diagram greatly
simplifies the task.
favorite technique counts the triangle not by shape, but by how many of the 6
star vertices are used. The surprising key observation is that there are NO
triangles that don't use one of these six points! The diagram's symmetry further reduces the search space, and
the counting turns out to be pretty easy.
each technique requires accurate searching and bookkeeping. From talking with a
number of the finalists, the most common oversight was missing some of the large
triangles that included two vertices.
competition produced some interesting statistical tidbits. Without
editorializing, here are the items that were the most interesting to me:
was solved by each of the 80 competitors.
was solved by only one: Julien Cassaigne of France.
teams didn't make it to the first of four milestones in Part III, Multi-Level
Rolling Block Maze, even though the solution for this was given in the
Part VI, it was the best teams that asked for hints, while the teams placing
15th, 16th, 17th, and 19th
ironically didn't ask for any help.
Huang solved 66 out of the 72 puzzles correctly. Ok, I will editorialize--this
performance was truly amazing!
hope that everyone enjoyed these puzzles as much as I have. I've had the (un)enviable
task of solving each of the puzzles, many of them multiple times. And I'm still
not tired of them! I think this is a great tribute to the many designers who
contributed their hard work to make the competition a success.
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