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Troll’s Challenge #68
Find the least significant digit of TREE(3).
And if you thought Graham’s Number was massive, this one dwarfs that real hard.
Troll’s Challenge #61
Find out who was the second-in-line and fourth-in-line to succeed the throne of Devanagara.
BACK YOUR ANSWER WITH A SOLID PROOF.
(The first one was Fujiwara no Iyozane, the third Fujiwara no Mitori, later Ooama no Ake no Mitori, and the fifth Fujiwara no Sanra, later Fujiwara no Shirogane no Sanra.)
Troll’s Challenge #57
Find out whether the Holy Lance of Antioch was the lance believed to have pierced Christ during the Crucifixion; an entirely different lance placed by someone else a long time previously; or buried on the spot shortly before its discovery.

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Troll’s Challenge #54
Construct the Euler line of an equilateral triangle with only a set of straightedge and compass.
Troll’s Challenge #53
Prove that the sum of all natural numbers is minus a twelfth without recourse to non-linear or non-stable summation methods.
(I only rated this nigh impossibru despite what Wikipedia says because I’m still waiting for the citation that asserts that it is indeed impossibru.)
Troll’s Challenge #45
In Diablo II, revive Frozen Horror-class enemies (Frozen Creeper, Frozen Terror, and Frozen Scourge).