//------------------------------//
// The Answer 1 
// Story: Life is a Test: A Series of Pony Logic Puzzles 
// by Brony_of_Brody 
//------------------------------//

It would take 11 ponies to go through all 2000 barrels.

First, you number all 2000 barrels from 1-2000. Then you assign each barrel a unique combination of testers to sample them.

In a simpler scenario with 4 barrels, you only need 2 testers, with each one testing each barrel as follows:

Nopony sups from Barrel 1.

Tester 1 sups from Barrel 2.

Tester 2 sups from Barrel 3.

Testers 1 and 2 sup from Barrel 4.

If they're both fine, Barrel 1 is the infected one. If only Tester 1 gets poisoned, it's Barrel 2 that's infected. If only Tester 2 gets pranked by the plant, it's Barrel 3. And if both testers get hit with Poison Joke, it's Barrel 4.

Working downwards, to test all 2000 barrels, the lowest number of ponies required is 11, for 2048 different combinations of testing. n testers requiring 2n combinations.