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If i have a shadow on the ground and i throw a shuriken at an enemy champion, if the first shuriken passes through minnions (thus its damage is reduced) does the second shuriken deal 50% of the reduced damage or 50% of the original damage?

5

Taken from the wiki:

ACTIVE: Zed throws his spinning blades forward, dealing physical damage to the first enemy they pass through and 60% damage to enemies thereafter.
「 PHYSICAL DAMAGE: 75 / 115 / 155 / 195 / 235 (+ 100% Bonus AD) 」
LIVING SHADOW: Active shadows also throw a shuriken in the direction of the target point. Additional shuriken striking the same enemy deal 50% damage and restore energy. 「 ADDITIONAL DAMAGE: 37.5 / 57.5 / 77.5 / 97.5 / 117.5 (+ 50% Bonus AD) 」

Because of:

Additional shuriken striking the same enemy deal 50% damage and restore energy.

It will deal the full damage if the shuriken hits a champion. However if it's hitting the same target, there is a damage reduction. Which is reduced later by enemy resistances.
EX. ( (100 * 0.5)*enemy resistance)
NOTE:

A shadow's shuriken will deal the full damage if hits a target before Zed's. In those cases, Zed's shuriken is the one that deals 50% damage. 

SOURCE: http://leagueoflegends.wikia.com/wiki/Zed
Also Zed Main since his launch.

0

The shuriken will do 50% of the original damage on the Q - enemy damage reduction

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