WPC2000

World Puzzle Championship 2000
(Scores for the WPC are posted at the official site.) I was a judge at the World Puzzle Championship. Before things even got started, I test solved dozens and dozens of puzzles. Nick Baxter, who organized the event, wanted to be sure that everything was fair and balanced. I was asked to be a judge by Will Shortz, and gladly accepted the task.

My first job at the Stanford Marriott was to greet people and hand them Sponsor packages. A book by David Tuller & Michael Rios was handed out -- Mensa Math & Logic Puzzles ($8). Many people were seen throughout the event trying the 380 puzzles in the book. There was a dinner that night, and all the teams were introduced. Meanwhile, my copy of Fill-agree by Kadon was hit with all that played with it. At the dinner, I met Bernardo Recaman Santos of Columbia. He gave me a great puzzle: Arrange the numbers 1-15 in a sequence with the property that every two consectutive numbers sum to a square number.

I went to Nick Baxter's room and started gluing puzzles together with him and Matthew Daly. We needed to finish them all in time for the Friday competition. Nick prepared labels for the board. Matthew had cut blocks and boards. Now we just needed to assemble everything. We ran out of glue early on, but fortunately there was a mall nearby. The object we constructed was a rolling block maze by Erich Friedman.

In Part 1, the potential champions solved a potpourri of 20 puzzles. I had a puzzle in that section. In the following four multiplication problems, each symbol stands for the same digit throughout. Figure out what number is represented by each symbol.

Another puzzle was Distance, by Erich Friedman. You need to put the numbers 1-15 into the unshaded circles so that the distances are constantly increasing. That is, the distance from 1 to 2 will be less than the distance from 2 to 3, which is less than the distance from 3 to 4, and so on. Here is my easy version of that puzzle.

Railroad Tracks was by Craig Kasper. 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 a cross. The track must go straight through the stations, which are the squares containing numbers. As you follow the track, you will visit stations 1 through 13 in order, then return back to station 1.

In Part II, solvers struggled with a set of Lunar Lockout problems. Here is a problem that was finally pulled for being 'too hard.' In this puzzle, the X robot is invisible. You must locate the only starting position of X so that a 7 move solution is possible.

Part III was the rolling block maze by Erich Friedman. It was quite a sight, watching 20 teams trying to solve a very interactive maze. You can see a picture of this maze above.

Part IV was a set of manipulative puzzles. Roundabout was by Adrian Fisher. Arrange the nine pieces to create an island containing a closed and continuous network of curved railroad track and roundabouts. No track runs off the edge of the island, there are no dead-ends, and there are no holes in the middle of the island.

There was also a Zome Construction problem by Nick Baxter and myself. Build K6 with 6 white nodes, 5 medium yellow struts, 2 long green struts, 1 short blue strut, 5 medium blue struts, and 2 long blue struts. After all the puzzles were over, I announced a $20 prize problem for Zome construction. Build the Petersen Graph with 15 short blue struts and 10 nodes. I'm not sure if this is solvable. I've managed 14 short blue struts, and miscellaneous struts for the last one.

Part 5 included 13 different variations of Battleships. Here is a variation that wasn't used -- Triangular Battleships. Locate the position of the 10-ship fleet in the grid. The fleet is shown to the right of the grid: one 4-unit battleship, two 3-unit cruisers, three 2-unit destroyers, and four 1-unit submarines. Each segment of a ship occupies a single cell. Ships are oriented either horizontally or vertically, and do not touch each other, even at a single point.

Part VI was Potato Appeal, a team solving competition put together by Wizards of the Coast. Mike Selinker wrote up the event, so I'll quote his write-up.

Mark Gottlieb and I spent the weekend at the 9th annual World Puzzle Championships, a major international event where teams from all over the world compete in puzzle solving. This year it was in the U.S. for the second time. The host country provides the puzzles for the competition, and so the organizers asked us to provide the major team competition-specifically the most memorable team competition ever.

A group of six Wizards R&D staffers (Mark and me, plus Richard Garfield, Teeuwynn Woodruff, Paul Peterson, and Mark Rosewater) enlisted the aid of Wayne Charness and Mark Morris at Hasbro Corporate to create a team event around Hasbro's own Mr. Potato Head. (We also had help from Andy Collins, Gwen Kestrel, Mons Johnson, Jayne Ulander, Darla Willis, and Brian Tinsman.)

Teams from 23 nations solved 12 complex puzzles, including a maze on Magic: the Gathering cards and a jigsaw on the bottoms of old DragonStrike figurines. Those puzzles led to numbers which allowed the team to try to assemble the "correct" Mr. Potato Head from an assortment of body parts.

The participants had never seen a competition like this. The sight of some of the smartest people in the world struggling to get a Mr. Potato Head exactly right was quite humorous. They realized early on that we were packing curveballs, as no less than eight teams (including the highly respected Czech team) insisted we had made several mistakes in Paul's paint-by-numbers puzzle, which just happened to be in base five rather than base ten. Still, teams leapt to amazing insights, such as when both the Australians and the Turks used the transparent Mr. Potato Head Silly Suitcase as a base to assemble Teeuwynn's figurine jigsaw-one person moved the DragonStrike pieces around on the top of the suitcase, while the other looked up from the floor to tell his partner where to move the pieces.

Over the first of two-and-a-half hours, these four-person teams breezed through some of the easier puzzles, such Richard's card maze and balloon balancing puzzle. Nobody got an advantage over another team, because the puzzles were both language and culture-neutral. For example, Mark G. constructed a fill-in puzzle using the names of obscure Hawaiian cities and towns. If anyone there spoke Hawaiian, they'd have a slight advantage. No one did.

At the end, the Potato Head competition came down to three teams: the Dutch, the Americans, and the French. The Dutch team solved their puzzles through careful management of hints from the judges, which cost them points. When they couldn't figure out a way into a puzzle, such as Mark G.'s unfathomably hard number blocks, they beelined toward the hints table. This meant that they had their solutions in plenty of time to assemble the potato. But an inability to solve one puzzle, Mark R.'s matching dice, meant they were missing information to solve the potato. They were off by several pieces (the eyes and the glasses, I think). And their stockpiling of hints meant that without the correct potato, they would be way behind the other successful teams.

The U.S. team solved much more methodically, and refused to take hints up till the end. They cracked their last puzzle (the blocks) with 6 minutes to go, too little time to solve the puzzle which gave the correct potato pieces. In a flurry of activity, they assembled one of many possible potatoes in the last few seconds. Naturally, they were wrong. But they solved all twelve other puzzles with the fewest hints (two), meaning that if no team correctly solved the potato, they'd win.

The French solved instinctively, at one point making an amazing (and correct) intuitive leap on a puzzle of mine. I did a 10-by-10 grid in which you had to insert 10 10-digit numbers across and down. The French team looked at me and thought, "Okay, they could've laid the ten numbers out in a lattice, meaning no horizontal numbers would touch each other, and no vertical numbers would touch each other. But these guys are kookier than that. What would happen if we assumed that they stuck three numbers together in a clump?" Of course, we had. So the French saved themselves probably 15 minutes of guesswork on that puzzle just by figuring out my personality.

With a good 20 minutes to go, the French had solved all but Mark G.'s bicycle-placement puzzle. This was one of the few puzzles in the competition that looked like a familiar puzzle type, the Minesweeper game. Two French competitors gave up on the puzzle and passed it to a third teammate, but they didn't bother to tell him the instructions to the puzzle. The new solver assumed it was a different kind of puzzle, and solved half of the puzzle incorrectly. So with 15 minutes to go, they solved for all the pieces on the Mr. Potato Head-except one. Their error on the bicycle puzzle left them with two choices for the mustache. They had a 50-50 chance to pick the right one, and as the last second expired, they grabbed the purple handlebar mustache and trusted their chance to fate. If
they were right, they'd get 350 more points, and would beat the Americans.

Three cheers for the red, white, and blue (ours, not theirs). The French team chose the wrong mustache, and the Americans won the team competition by the hair on Mr. Potato Head's nose.

The organizers and the competitors were unanimous in their appreciation for what they thought was the most inspired team competition in WPC history. We received an ovation at the closing ceremonies. All the teams took their Mr. Potato Heads home, including the delighted daughter of one of the Swiss competitors.

There was a highly contested individual competition as well. In recent years, the competition has been dominated by American electrical engineer Wei-Hwa Huang, who won four of the last five individual championships. Again the heavy favorite, he went into the final round of the competition with an unprecedented high score. The tournament is built so that your score over the preliminary five rounds of puzzles converts to a number of seconds head-start over your competitors in the final round. The 10th place competitor has 30 minutes, and each higher-scoring competitor has a bonus time over 30 minutes. The competition organizers expected that the leader might get a bonus of 4 or 5 minutes over the 10th place competitor.

Terrifyingly, Huang went into the finals with a 26-minute head-start over the 10th place competitor, and an 11-minute head-start over the 2nd place competitor. We feared that Huang would be done before the 10th place competitor even started. Sure enough, he solved three of the eight puzzles before his nearest competition even stood up.

The competitors wore headphones, and for additional sound-baffling they piped U.N. Security Council dialogue over the loudspeakers during the finals. They couldn't see each other's scores, so no competitor knew how any others were doing. But the judges knew, and more importantly, we knew that Huang had gotten one solution wrong in a triangle-counting puzzle. This could be his undoing, because a single wrong solution would drop him below anyone who got all the right answers, no matter how early his solutions came in. Huang stayed up there long after he turned in his final answer, checking and rechecking his results. And with only 1:45 to go, he turned in a new and correct solution to the triangle-counting puzzle. Now he had all the solutions correct.

But so did the 3rd place finalist, Ulrich Voigt of Germany, who started 14 minutes after Huang. More importantly, he turned in his last correct solution with 3 minutes to go. So in a huge upset, Voigt leaped from 3rd to 1st and captured the individual goal medal. Huang was very gracious about his defeat, and will surely be the favorite next year in the Czech Republic. After all, now he has something to prove.

On a personal level, I met some international paragons of puzzlemaking. I met Tetsuya Nishio, the creator of the internationally popular paint-by-numbers puzzle type. I was surprised that when we were introduced by a translator, he said in Japanese, "Michael Selinker of Games Magazine?" That was a great honor. He especially liked the base five paint-by-numbers, even though he was one of the people who assumed we'd made a mistake in the design of the puzzle. Tetsuya gave me a Japanese puzzle book, and I gave him Mark G.'s copy of AlphaBlitz.

I also met Akio Kamei, another Japanese who is the world's greatest creator of wooden block puzzles. He also didn't speak English, but we communicated through translators. (I later asked my Japanese translator whether Tetsuya and Akio knew each other. He said that they knew each other by reputation, but that there was a divide between creators of paper puzzles and creators of physical puzzles in Japan. Sort of an East Coast-West Coast rap thing, I guess.)

The American luminaries were there too. I met Jerry Slocum, author of many books and America's foremost expert on physical puzzles, who runs a museum down in California. The competition was hosted by Will Shortz, the NPR and New York Times crossword editor, who (along with competition director Nick Baxter) asked for my help in the making of the team competition.

Overall, it was a splendid weekend. I've never found puzzle competitions that exciting to watch, but this was truly satisfying all the way around. I hope I can be involved in another WPC competition somewhere down the line.

It was just as fascinating as M. Selinker says. The Balloon Balance problem by Richard Garfield is below. Note that the weights and balloons are in equilibrium on the smaller figure. Move them to the larger figure and obtain equilibrium. Of all the puzzles, I think this was my favorite.

Part VII was Optimization. Remember my Crossword Maze puzzle? Will Shortz rejected it 22 years ago, back when he worked for Games. I printed it here at my site, and Nick Baxter wanted it. Will Shortz wound up being one of the test solvers, and this time he liked it. Luc Kumps did a lot with Crossword Mazes, but I couldn't print any of it if I wanted to see them in the WPC. Here is my starting page for crossword mazes. The puzzle was to add one square, then find the longest possible path. I added a square to the lower corner, and beat everyone in the competition with the route below.

Another optimization challenge was to divide a Connecticut grid into squares. Denis Auroux of France managed to find a 64 square solution. His solving method was to "look for miracles." Can you match his feat? My own personal best was 79 squares.

Part X included more miscellaneous puzzles. My favorite from this batch was Triangle Trisection by Nob Yoshigahara. Divide the figure into three contiguous pieces that can be reassembled to form an equilateral triangle. Pieces can be rotated, but not reflected. The grid lines are given to show the true proportions of the diagram; your cuts may be anywhere. Only one person solved this. I managed to solve it in the test solving phase.

Judging all these puzzles took awhile. Particularly fun was the Connecticut grid, since we had to count squares on each entry. We got all the papers back by midnight. The next day, ten finalists were selected for a final round of puzzles.

The top ten solvers wore soundproof headphones as they faced the final round -- eight puzzles on posterboard. The tenth place person was given 30 minutes. Solvers with more points were given extra time. Wei-Hwa wound up with a 25 minute lead. The way the rules worked, an answer could be resubmitted, wiping out the previous submittal. Whoever submitted the most correct answers the earliest would win.

Other solvers gradually trickled in, until all ten raced the clock, trying to solve all the puzzles. Wei-Hwa carefully checked all his answers as the others solved the puzzles. With about two minutes remaining, Wei-Hwa realized he had made a mistake with a triangle counting problem. He submitted the correct answer. A few seconds earlier, Ulrich Voigt of Germany had submitted the final answer to his eighth puzzle, and thus became the World Puzzle Champion. Wei-Hwa Huang of the United States came in second. Niels Roest of the Netherlands came in third. The US team beat all others.

Here's the puzzle that gave Wei-Hwa trouble --

How many triangles are in this figure? (By Nick Baxter)

So, that was the World Puzzle Championship in a nutshell. There's still more I'll be adding to this page, but not tonight. If you have a write-up or puzzle you'd like to share, please write to me.

Composer's Competition For those that made the puzzles. Erich Friedman won with 18 varied puzzles. Nick Baxter tied for second, with 13 puzzles. He also organized everything. David Tuller & Michael Rios also came in second with 13 puzzles. Dave & Michael's book Mensa Math & Logic Puzzles ($8) is now available. It's a great book, stuffed with 380 puzzles.

Will Shortz came in fourth, with six puzzles. The other composers were Craig Kasper (4), Mark Gottlieb (4), Harry Nelson (4), Ed Pegg Jr (3), Scott Kim (3), Adrian Fisher (2), Richard Garfield (2), Mark Rosewater (2), Serhiy Grabarchuk (2), Mike Selinker (2), Teeuwynn Woodruff (2) Peter Grabarchuk (1), Nob Yoshigahara (1), Fred Piscop (1), Goh Pit Khiam (1), Moshe Rubin (1), Nancy Schuster (1), Sherlee Oldacre (1), Alexey Pajitov (1), and Paul Peterson (1). I'll try to present several of these puzzles after getting the necessary permissions.

I learned of Brein Brekers, a puzzle magazine from the Netherlands. I'll try to make a new page of puzzle magazines.