In Super Mario Bros, there is a glitch, where a certain set of frame-perfect presses allow you to jump directly into the bottom block of the flagpole at the end of the level. In this article on the Mario Wiki, it describes the glitch as:
The player must jump right next to the block that holds the Flagpole and then jump again. If done correctly, Mario or Luigi will jump onto the flagpole normally, but the flag will remain raised.
The article also provides an animation for reference:
(source: mariowiki.com)
TASVideos describes the glitch as:
Complete the level without lowering the flag by glitching into the base block of the flagpole and touch the flapole from inside. Doing so is faster than lowering the flag. The points you get from the flagpole will be only 100. This trick isn't used in 8-3 of the warped run, since the timer would turn 343 which results in fireworks. The flagpole glitch was originally found by klmz.
Unfortunately, I cannot find a better explanation of how to cause the glitch than either of these articles. Any help on how to trigger this glitch would be greatly appreciated.
Best Answer
I've found a pretty good explanation of how to pull off this glitch in this thread:
I found an attempted explanation by the first person to successfully pull off a flagpole glitch in this thread. The explanation is for the flagpole glitch on 8-2, so it mentions a Bullet Bill, but the rest applies to the flagpole glitch in 1-1.
I also found a tutorial of how to do this in a TAS and it even includes a video.