Call the slaves a,b,c,d,& e Each slave (5 - a,b,c,d,e) drinks from 16 barrels - 80. Each unique pair (10 - ab,ac,ad,ae,bc,bd,be,cd,ce,de) drinks from 8 barrels

Call the slaves a,b,c,d,& e Each slave (5 - a,b,c,d,e) drinks from 16 barrels - 80. Each unique pair (10 - ab,ac,ad,ae,bc,bd,be,cd,ce,de) drinks from 8 barrels - 80. Each unique trio (10 - abc,abd,abe,acd,ace,ade,bcd,bce,bdc,cde) drinks from 4 barrels - 40. Each unique quartet (5 - abcd,abce,abde,acde,bcde) drinks from 2 barrels - 10. Everyone (5 - abcd) drinks from 1 barrel - 1. Nobody drinks from remaining 9 barrels - 9. If 1 slave dies we have 16 suspect barrels Each remaining slave (4), pair (6), trio (4) and quartet (1) drink from 1 barrel - 15 If 2 slaves die we have 8 suspect barrels Each remaining slave (3), pair (3), and trio (1) drink from 1 barrel - 7 If 3 slaves die we have 4 suspect barrels Each remaining slave (2), pair (1) drink from 1 barrel - 3 If 4 slaves die we have 2 suspect barrels The remaining slave drinks from 1 barrel If 5 slaves die we have a positive ID on the barrel If 0 slaves die we have 9 suspect barrels Each remaining slave (5) and 3 pairs drink from 1 barrel - 8