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The Best Way to Look Through a WHERE’S WALDO? Book, Mathematically

The Best Way to Look Through a WHERE’S WALDO? Book, Mathematically

Trying to find the bespectacled and candy cane colored goof in the Where’s Waldo? books was always fun…for about five minutes. After that, you got frustrated. You devised a grid pattern that spanned the two colorful and chaotic pages and methodically searched for Waldo. When you finally did locate the man, it was more relief than anything.

Randal S. Olson is a Computer Science & Engineering Ph.D. candidate at Michigan State University who found himself with time to spare while snowed in at his home. Like any sensible individual, he decided to spend that time determining the most mathematically sound searching path for all seven primary Where’s Waldo? books. You know, like you do.

The impetus to do so came from an old Slate article that claimed to have found the best path through any Waldo book. Olson thought the advice was all right, but it could use a bit more rigor. Olson started by mapping out the 68 Waldo locations across all books on two pages (Waldo was found in the top right of the second page, etc.).

WaldoSearch_Locations

From this a few trends popped out. First, Waldo would almost never be in the top left of the page, as this is where a postcard filled with information would be. Second, Waldo doesn’t hide near the edges, perhaps because that’s where we scan first (like trying to start a jigsaw puzzle). Third, Waldo is never located in the bottom right of the second page, because, as Olson speculates, that’s the area you see immediately after flipping to a new page.

With these trends in mind, Olson started his analysis.

What Olson wanted to find was the path that would check every possible location for Waldo in the least amount of time. However, if you did that randomly – checking each possible path across the 68 locations – it would take you longer than the age of the universe. Much longer. No, to check Waldo’s possible hiding places, Olson used something much more powerful: evolution.

A genetic algorithm is a mathematical expression that starts by trying a number of possible solutions and then starts weeding out the solutions that don’t work as well. By constantly trying new solutions against the current best solution, a genetic algorithm can “evolve” to be nearly perfect very quickly. The same kind of process happens with life – randomly adding onto what already works and keeping the improvements – but on a much longer timeline.

In five minutes, Olson’s genetic algorithm had a near-perfect search path for finding Waldo in the shortest amount of time. It looked like this (the different colors denote different fourths of the path):

WaldoSearch_GIF

Olson figures that if you use this optimal path, you could find Waldo on any page of the original seven books much faster than the traditional “search until consumed with page-tearing rage” method.

WaldoSearch_Optimal

Given the trends from the Waldo locations and the genetic algorithm’s path, Olson put together the best search path above. Of course, as he mentions, this isn’t necessarily the “fun” way to read a Where’s Waldo? book. He writes, “I don’t recommend actually using this strategy for casual Where’s Waldo? reading. As with so many things in life, the joy of finding Waldo is in the journey, not the destination.”

But I’ll be damned if I don’t challenge the next kid I see with one to a race.

Kyle Hill is the Science Editor at Nerdist Industries. Follow on Twitter @Sci_Phile.

IMAGES: All images reproduced with permission from Randal S. Olson.

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Comments

  1. Beautiful and amazing Thanks for sharing

  2. Alex Rodriguez says:

    Some people have way too much free time on their hands.