Hello! I have multiple different files with different sizes, I want to move files from disk 1 to disk 2, which has only 688 space available. Without yapping, and being as concise as possible. What combination of files gets me closer to that number? The file sizes are: 36, 36, 49, 53, 54, 54, 63, 94, 94, 107, 164, 201, 361, 478

Alright, so I have to figure out which combination of these files to move such that the total comes as close as possible to 688 without exceeding it. Let me think through this step by step.

First, let's list all the files again to have them clear: 36, 36, 49, 53, 54, 54, 63, 94, 94, 107, 164, 201, 361, 478.

Hmm, that's 14 files. I need a combination that adds up as close as possible to 688. Since this is a subset sum problem, maybe starting with the largest files first could help because they contribute more to reaching the target. Let me try that approach, but I should be cautious because sometimes smaller files can fill in the gaps better.

Starting with the largest file, which is 478. If I take that, then I need to make up the remaining 688 - 478 = 210 with other files.

Looking at the remaining files after 478, the next largest is 361. But 478 + 361 = 839, which is way over 688. So that's not good. So maybe skip 361 for now.

Next is 201. Let's see 478 + 201 = 679. That's under by 9. Then maybe adding smaller files? Let's see: 679 + 9 = 688, so maybe 9? Wait, but we don't have a 9. The next is 36. Adding 36 would make it 715, which is too much. Hmm, so maybe the combination of 478 + 201 is 679, which is 9 less than 688. But is there a better option?

Alternatively, maybe not using 201. Let's see: 478 plus other files. Let's see 164. 478+164 = 642. That leaves 688-642 = 46. The smallest files available here are 36 and smaller. So 642 + 36 = 678, or 36+36 = 72 but that would exceed. 36+36=72 added to 642 would be 714, which is too big. Hmm. Alternatively, 49, so 642 + 49=691, which is over. So maybe adding 36 gives 678, which is 10 less. Or maybe another combination. Alternatively, 478 + 107 + let's see 107 makes it 478+107=585, so then adding 201? 585+201=786, too big. Maybe 478 + 107 + 94? 478+107=585; 585+94=679, same as before. Hmm, same result. Maybe 478 + 107 + 36= 478+107=585 +36=621, then need 67 more? Not sure.

Alternatively, maybe not taking 478. Let me see if excluding the 478, maybe a better combination. Let's see: starting with the next largest after 478 is 361. So 361 and then what? 361 + 201 = 562. Remaining space: 126. Then, adding files like 94 (562+94=656). 688-656=32. Not enough. 656 + something else? 36 (total 692 over). Hmm.

Or 361 + 164 = 525. Then remaining 688-525= 163. Maybe 164 isn't needed then. Wait, maybe I need to think differently. Let me recast.

Let me try to try 478 + 201 (679), that's 679. Then, maybe the difference is 9, but I can't get that. Alternatively, combine 478 with some other files to get closer.

If instead of 201, maybe use a smaller file. Let's see:

478 + 164 = 642, then 46 left. We can take a 36 and 9 (not available), so maybe 36 + 9 (no, 9 isn't there). So just 36 would be 678.

Alternatively:

478 + 49 + 54 (478+49=527, +54=581). Then maybe add 94? 581 +94= 675, then add another 13 (no). Or 675 + 13? Not possible. Alternatively, adding another 94, but that's two 94s. Wait, there are two 94s. So 478 + 94 +94 = 478+188=666, which plus something else. 688-666 = 22. Can't get. Hmm.

Alternatively, 478 + 107 + 63? 478+107=585+63=648, then 40 left. Maybe 36 +4. Not. 36 gives 648+36=684, which is 4 less. That's better than 679. So 478+107+63+36= 684. So that's 684. Which is within 4 of 688. Maybe that's better than previous options?

Alternatively, maybe 478+107+94? 478+107=585 +94=679. So that's back to 679.

Hmm. 684 is a better hit because it's closer.

Wait another approach: what if we don't include 478? Let's see: 361 + 201 = 562. Then 126 left. 94 + something. 562+94=656. 656 + 20? Not. 656 +36=692 (over). So maybe 656 is still under. 656+ the other 36 would still exceed.

Alternatively 361 + 201+94. Wait, 361+201=562 +94 is 656, as before.

Alternatively, 361 + 164 =525, plus 94: 525+94=619. Then 169 left. 164? But that's already included. Hmm.

Alternatively, maybe 201 is a good candidate. Let's see if we can make a combination with 201, 164, 94, etc.

Alternatively, 478 is a large file, so maybe using it is better. Let me see if there's a better combo with it.

Trying 478 +164 + 107 = 478+164=642 +107=749 (over the limit). So that's too big.

Hmm. How about 478 + 201 + 63: 478+201=679 +63=742 (over). No.

Alternatively, 478 + 201 + (then what? Let's think).

Wait, so the earlier idea of 478+107+63+36 = 684. That's pretty good. Are there other combinations?

Let me see another path. Let's try starting with 361 and 201. 361+201=562. Now remaining 688-562=126. Can I get 126?

Looking at the remaining files: 36,36,49,53,54,54,63,94,94, 107, 164. Wait, but 201 and 361 are already used. So the rest are 36,36,49,53,54,54,63,94,94,107,164,478.

Wait, no. Wait, the original list included all those, so after taking 361 and 201, the remaining available files (excluding those two) would be 36,