AWOKK, Day 3: KenKen Times

September 21, 2016 at 5:05 am Leave a comment

Today is Day 3 in MJ4MF’s A Week of KenKen series. In case you missed the fun we’ve had previously…

Yesterday, I introduced you to the KENtathlon.

While completing a KENtathlon, my goal is to complete a 6 × 6 puzzle in less than 2 minutes; a 5 × 5 puzzle in less than 1 minute; and a 4 × 4 puzzle in less than 20 seconds. Even though the sum of those times for all three puzzles is 3 minutes, 20 seconds, my goal is a combined time of 3 minutes. It’s good to have goals.

Puzzle Size Goal Time Personal Best
4 × 4 0:20 0:12
5 × 5 1:00 0:27
6 × 6 2:00 1:29
KENtathlon 3:00 2:32

 

I don’t always perform well enough to meet those goals. And when I don’t, I repeat the same size puzzle again… and again… and again… for as many attempts as it takes to complete each puzzle in the allotted time. And when I’ve met the time goal for each puzzle individually, if the combined time isn’t satisfactory, then I start the whole thing over.

To say that I’m slightly obsessive would be like saying that the Pope is a little bit Catholic.

As you may have noticed in the table, I once finished a 4 × 4 puzzle in 12 seconds. The key word there is once. The stars were in alignment that day — it was an easy puzzle, and the dexterity of my thumbs and fingers was at an all-time high. Though I’ve attained 13 a handful of times, I’ve never replicated that 12-second feat.

12SecondKenKen

My fastest puzzle ever,
not Photoshopped.

 

That said, I regularly complete 4 × 4 puzzles in 14 or 15 seconds. With that being the case, you have to wonder if the 20-second goal is really a challenge. And what about the goal times for 5 × 5 and 6 × 6 puzzles?

Admittedly, my time goals are arbitrary, though not random. When I chose those goals, I had completed enough KenKen puzzles that I intuitively knew what felt right. Still, it wasn’t based on hard data… and if you’ve read this blog long enough, you know that that bothered me. A lot.

But what’s a boy to do?

I suppose a well-adjusted human might do nothing, think it’s not worth the trouble, and just let the whole thing go. But an obsessive numbers guy? Well, he’d painstakingly solve 132 KenKen puzzles, collect data on the amount of time each one took to complete, meticulously record the data in an Excel spreadsheet, and perform a thorough analysis. You may think that undertaking such a project is ludicrous; but to me, it was absolutely essential.

The graph below shows the results. The circular dots represent my median time for each puzzle size, and the square dots represent the upper and lower quartiles. For instance, the median time for 6 × 6 puzzles was 217 seconds, while the interquartile range for 6 × 6 puzzles extended from 163 to 284 seconds.

KenKen Time RegressionWhat this reveals is that my intuition wasn’t perfect, but not bad.

  • I completed 49% of 4 × 4 puzzles in less than the goal time of 20 seconds.
  • I completed 58% of 5 × 5 puzzles in less than the goal time of 1 minute.
  • But, I completed only 14% of 6 × 6 puzzles in less than the goal time of 2 minutes.

Further analysis revealed that I completed 40% of the 6×6 puzzles under 3 minutes, and that seems a bit more reasonable, so my new goal time for 6 × 6 puzzles is 3 minutes.

Now, I know you thought this analysis was completely unnecessary, but the proof is in the pudding. The results were invaluable. By considering the data, interpreting the results, and revising my goal time for 6 × 6 puzzles, the probability that I can now complete each size puzzle in the allotted time on the first or second try has increased from 16% to 39%. Or said another way, Remy’s morning walks now last an average of just 15 minutes, whereas some of them used to take an hour-and-a-half.

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AWOKK, Day 2: The KENtathlon AWOKK, Day 4: My Puzzles

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About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

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