# How many artifacts will be left with her when she reaches her destination crossing all the check points ?

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Anya is a clever trader of rare artifacts. Each day she carries three boxes with each filled with thirty artifacts. The boxes cant hold more than that. She travels far of northern lands to sell these artifacts but on way, she comes across thirty checkpoints where she has to shed one of the artifact for each sack to the authorities for letting her pass.

How many artifacts will be left with her when she reaches her destination crossing all the check points ?

posted Sep 14, 2018

If B1, B2 & B3 are the boxes
{ My approach:
1. B1-B2-B3
2.#-B2-B3-B1
3. #-#-B3-B1-B2
& so on }

Steps
1. B1 (29 Artifacts)(1 Checkpoint) B2 (28 Artifacts)(2 Checkpoint) B3 (27 Artifacts)(3 Checkpoint)
2. B2 (28 Artifacts)(2 Checkpoint) B3 (27 Artifacts)(3 Checkpoint) B1 (27 Artifacts)(4 Checkpoint)..........
17. B3 (21 Artifacts)(12 Checkpoint) B1 (21 Artifacts)(13 Checkpoint) B2 (20 Artifacts)(14 Checkpoint)
18. B3 (11 Artifacts)(13 Checkpoint) B1 (30 Artifacts)(13 Checkpoint) B2 (20 Artifacts)(14 Checkpoint)
19. B1 (30 Artifacts)(13 Checkpoint) B3 (0 Artifacts)(14 Checkpoint) B2 (30 Artifacts)(14 Checkpoint) [ B3 is left behind]
20. B2 (30 Artifacts)(14 Checkpoint) B1 (28 Artifacts)(15 Checkpoint) ........
34. B2 (16 Artifacts)(28 Checkpoint) B1 (14 Artifacts)(29 Checkpoint)
35. B2 (29 Artifacts)(29 Checkpoint) B1 (0 Artifacts)(29 Checkpoint) [B1 is left behind]
36. B2 (28 Artifacts)(30 Checkpoint)

So in the end, Anya can manage to bring 28 Artifacts with her after the 30th checkpoint if she doesn't mind going back and forth a lot to save just 3 boxes more.

There is another simpler approach to this that can manage to save 25 Artifacts at the end
1. Carry all the 3 boxes till the 10th Checkpoint (20, 20, 20). Now take the 20 from the 1st box and split 10 each to the remaining 2 boxes (0, 30, 30)
2. Carry the 2 boxes till the 25th Checkpoint (15, 15) Now Empty 1 box onto another (0, 30)
3. Carry the 1 box to the end (30th) ==> 30 - 5 = 25 Boxes available at the end.

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