For decades Waldo has eluded millions of children in the classic book series - and he’s likely frustrated a number of adults too.

To make finding the bespectacled character easier, a Michigan-based computer scientist has devised a strategy using machine learning and algorithms.

By plotting Waldo’s location across the series, Randal Olson created the path needed to travel around a typical page and find Waldo in the quickest way possible each time.

Mr Olson used an algorithm to approximate the ‘optimal search path’ (pictured). He then divided the path into four sections, the first part is shown in blue, the second is orange, the third is green and the final section is shown in red. This path represents one of the shortest possible paths to follow on the page to find Waldo

The method built on a previous strategy by Ben Blatt from Slate magazine in November 2013. During this research, Mr Blatt plotted Waldo’s 68 locations across seven books.

Mr Olson took these plots to create a so-called kernel density estimation. This established the probability of Waldo being found in certain parts of a page.

From this, Mr Olson discovered that Waldo is rarely located in the top left-hand corner, or along the edges, to account for the box that typically described the setting and for printing inconsistencies.

Waldo was also never found on the bottom of the right-hand page.

Next, Mr Olson used what is known as the ‘travelling salesman problem’ to check every possible Wally location in the shortest time possible, with the least repetition.

By following this method, Mr Olson was able to ‘zoom through most illustrations’ (example pictured) in less than 10 seconds. He also discovered that on at least four occasions, book one in particular had instances or ‘outliers’ in which the strategy didn't work

‘In computer terms, that means we’re making a list of all 68 points that Waldo could be at, then sorting them based on the order that we’re going to visit them,’ explained Mr Olson on his blog.

‘Those 68 points can be arranged in ~2.48 x 1096 possible ways. To provide some context, that’s more possible arrangements than the number of atoms in the universe.’

Due to the complexity of the task, Mr Olson used machine learning to approximate the ‘optimal search path’ based on an algorithm.

To make finding Waldo - known as Wally in the UK - easier, a computer scientist plotted all of the character's 68 locations across seven of the classic books (pictured). The method built on a previous strategy created by Ben Blatt from Slate magazine in November 2013

HOW TO FIND WALDO QUICKLY Randal Olson used an algorithm to plot the shortest path required to find Waldo (pictured). But also revealed tips to make the process easier Randal Olson used an algorithm to plot the shortest path required to find Waldo. But, Mr Olson acknowledged that humans are unable to remember a path as easily as a computer and revealed tips to make the process easier. Waldo is rarely located in the top left-hand corner, or along the edges, for example. He is also rarely found on the bottom of the right-hand page. Start on the bottom half of the left-hand page.If Waldo isn’t on the bottom half of the left page, 'then he’s probably not on the left page at all'. The upper quarter of the right page is the next best place to look and Mr Olson said 'Waldo seems to prefer to hide on the upper quarter of the right page.' Next check the bottom right half of the right page. Mr Olson added Waldo has an aversion to the bottom left half of the right page and searchers shouldn't bother looking there until they're exhausted the other hot spots. Advertisement

He ran this algorithm for five minutes and created a solution that divided the path into four sections: the first part is shown in blue, the second is orange, the third is green and the final section is shown in red.

‘This path represents one of the shortest possible paths to follow on the page to find Waldo,’ continued Mr Olson.

‘So if we followed this path exactly, we’d most likely find Waldo much faster than someone following a more basic technique.’

But, Mr Olson acknowledged that humans are unable to remember a path as easily as a computer and revealed tips to make the process easier.

He said searchers should start on the bottom half of the left-hand page and if Waldo isn’t on the bottom half of the left page, 'then he’s probably not on the left page at all'.

Mr Olson used these locations to create a kernel density estimation (pictured) and establish the probability of Waldo being found in certain parts of a page. From this, Mr Olson discovered Waldo is rarely located in the top left-hand corner, or along the edges. He was also never found on the bottom of the right-hand page

To create the path, Mr Olson ran an algorithm for five minutes (demonstrated) to find the solution

The upper quarter of the right page is the next best place to look and Mr Olson said 'Waldo seems to prefer to hide on the upper quarter of the right page.'

Next check the bottom right half of the right page.

Mr Olson added Waldo has an aversion to the bottom left half of the right page and people shouldn't bother looking there until they're exhausted the other hot spots.

By following this method, Mr Olson was able to ‘zoom through most illustrations’ in less than 10 seconds.

He also discovered that on at least four occasions, book one in particular had instances or ‘outliers’ in which the strategy didn't work.

‘This was all done in good humour and I I don’t recommend actually using this strategy for casual ‘Where’s Waldo?’ reading,' concluded Mr Olson.

‘As with so many things in life, the joy of finding Waldo is in the journey, not the destination,’



