The Orbs solution is Incomplete Well, it really inst' a sloution, if it doesn't describe how you get to find that sequence, the reasoning behind it. Also where it states: (n'+1 .. n'-1) should be: (n'+1 .. n-1) Rui Martins Wednesday, August 04, 2004 Here's the rationale: Let M be the total maximum number of drops required for both orbs.  If orb 1 breaks on try 1, orb 2 may be dropped at most M-1 times.  This requires that orb 1's first drop be from no higher than floor M. If orb 1 breaks on try 2, we may drop orb 2 at most M-2 times.  Thus orb 1's second drop would be M-1 floors above the first drop, or floor M + (M-1). In general, if orb 1 breaks on try n then orb 2 is allowed at most M-n drops, and the corresponding nth floor number is: F(M, n) = M + (M-1) + (M-2) + ... + (M-n+1) Note that n cannot exceed M, so the highest floor testable is : F(M, M) = M + (M-1) + (M-2) + ... + (M-M+1) = (1 + 2 + ... + M) = M(M+1)/2 We need to test at least to floor 100, so we require F(M, M) >= 100 : or M(M+1) >= 200 14 is the smallest positive integer satisfying this requirement. The corresponding floor sequence would be: 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, 102, 104, 105 Since there are only 100 floors, the sequence ends: ..., 95, 99, 100. Chuck Boyer Thursday, August 05, 2004 There's a sense in which the given solution can be improved slightly. The given solution was 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 99, 100 Now drop the first orb on the successive floors in this sequence and suppose that we have just dropped the orb from floor 95 without breaking.  Now if we continue with floor 99, we could take as many as four more drops to find the desired floor -- drop 99 and breaks, then 96, 97, and 98.  If we drop orb 1 from floor 98 instead, we can reduce this to at most three drops. There are two possibilities. Scenario 1: 98 breaks and then 96, 97. Scenario 2: 98 doesn't break and then 99,100 Hence, the "best" solution should really be 14, 27, 39, 50, 60, 69, 77, 84, 90, 95, 98, 99, 100 Glenn C. Rhoads Friday, August 27, 2004   Fog Creek Home