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The original gameboy, GBP and GBC all had screen resolutions of 160x144[1] while the Game Boy Advanced had a resolution of 240x160[2]

So how does the actual stretching occur? It seems pretty uniform, but I can't wrap my head around how it's technically achievable without a second screen.

Firstly, the stretching isn't done in the vertical direction: Game Boy (and Color) games only used 144 rows of the 160 available on Advance screen, so there'd be black "letterbox" bars at the top and bottom, whether you stretched the image widescreen (with the shoulder buttons) or not.

Horizontally, the image is definitely stretched. If the Advance had twice the horizontal resolution of the Game Boy, it would be easy to stretch: each column of pixels could be repeated twice. It would effectively mean that each of the Game Boy's pixels were twice as wide as before. It's not always feasible to double the resolution of your screen; it's likely that such a resolution wasn't available (or affordable) in a handheld size at the time of the Advance.

Instead, Nintendo selected a screen for the Advance that had a resolution that is one and a half times that of the original Game Boy (160 x 1.5 = 240). The two resolutions have a lowest common factor of 3, which means that a "new" column of pixels can be inserted in every third column to scale the game to widescreen. In other words, every two columns of original screen needs to be "stretched" over three columns.

But what values should be assigned to the pixels in these extra third columns? You could double up some of the original columns' pixels, doubling the "width" of all the odd columns, or perhaps the even ones. It's a simple method, but doesn't look that good, because some columns won't be doubled at all, but others will.

An alternative approach is to use a technique called interpolation.[*1] In this instance, rather than choosing to duplicate one column to fill the empty pixels, you take an average of the values in the columns to the left and the right of each empty pixel, and use this calculated value instead.

If you look closely at the Advance's display with an un-stretched Game Boy game, then a stretched one, it's possible to identify which columns have had their values calculated by this "averaging" interpolation.

If Nintendo hadn't chosen a resolution for the Advance that had such a low common factor with the Game Boy, the interpolated columns would be at less regular intervals. Some of the Game Boy's original columns would be next to the new interpolated columns, but others wouldn't. This would have the effect that sprites (e.g. Mario) and details on them would become slightly narrower and wider as the traveled across the screen. This would be distracting, and look unattractive.

1. This technique is used when you resize a picture in image manipulation software such as Photoshop or GIMP. It's also used on computer LCD displays, if you select a resolution (e.g. 640x480) that doesn't match the display's native resolution (e.g 1024x768).