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A very simple technique with an over-dramatic name, One Thousand Years of Death is little more than inserting one's index and middle fingers (similar to the Tiger hand seal) into the opponent's rectum, causing constipation, pain and/or embarrassment. It has no effect on unconscious targets. Characters that see the jutsu react oddly (Temari blushes, Pakkun questions if it's really a jutsu, and Gamakichi shows a look of disappointment), while those who have used or experienced the jutsu show great fear in it being used on them.
While seemingly useless, the technique can be useful if used correctly. During the first bell test, Kakashi was able to throw Naruto a great distance, probably propelling him with chakra. Naruto would later find out that the point behind the technique was to target the opponent's blind spot, and when one substitutes their fingers for a kunai with an exploding tag, it can be a lethal technique. The aforementioned variant has only been used by Naruto.
This jutsu's full name is "Konohagakure Hiden Secret Taijutsu Technique: One Thousand Years of Death" (木ノ葉隠れ秘伝体術奥義・千年殺し, Konohagakure Hiden Taijutsu Ōgi: Sennen Goroshi, Viz: Konohagakure's Most Secret and Sacred Technique: One Thousand Years of Death, English TV: Hidden Leaf Village Secret Finger Jutsu: One Thousand Years of Death, UK DVD: Secret Ninja Technique of the Hidden Leaf School, Death for 1000 Years, English Games "Sacred Taijutsu: 1000 Years of Death")
The official name for this technique is Sennen Goroshi. However, the name is sometimes thought erroneously to be Sennen Gurushi (千年苦し), meaning something along the lines of "Thousand Years of Pain".
This technique is modelled after the Kancho, a Japanese prank of common usage among children. When Kakashi first performed it, it might have been a simple kancho with a jutsu-like name, which Naruto would believe to be a real jutsu, eventually leading to its usage in real combat.