# Solid Gold!

You'll need a total of 51 "gold" bars taken from the seven vaults as follows: 1 bar from the first vault, 2 bars from the second vault, 4 bars from the third vault, 7 bars from fourth vault, 13 bars from the fifth vault, 24 bars from the sixth vault, and 0 bars from seventh vault.

51 gold bars should weight 510 kilograms (ouch!). But they'll inevitably weigh less than that, because three vaults contain counterfeits. Depending on which vaults contained fakes, you'll see different deficits. For example, the heaviest the scale could read would be 507. And if it did, it's light 3 pounds. The only combination that could yield that amount is 0 + 1 + 2, or the first, second and seventh vaults.

Below are all the possible vault permutations, proving that each combination is unique:

3 = 0 + 1 + 2           5 = 0 + 1 + 4          6 = 0 + 2 + 4
7 = 1 + 2 + 4           8 = 0 + 1 + 7          9 = 0 + 2 + 7
10 = 1 + 2 + 7        11 = 0 + 4 + 7        12 = 1 + 4 + 7
13 = 2 + 4 + 7        14 = 0 + 1 + 13      15 = 0 + 2 + 13
16 = 1 + 2 + 13      17 = 0 + 4 + 13      18 = 1 + 4 + 13
19 = 2 + 4 + 13      20 = 0 + 7 + 13      21 = 1 + 7 + 13
22 = 2 + 7 + 13      24 = 4 + 7 + 13      25 = 0 + 1 + 24
26 = 0 + 2 + 24      27 = 1 + 2 + 24      28 = 0 + 4 + 24
29 = 1 + 4 + 24      30 = 2 + 4 + 24      31 = 0 + 7 + 24
32 = 1 + 7 + 24      33 = 2 + 7 + 24      35 = 4 + 7 + 24
37 = 0 + 13 + 24    38 = 1 + 13 + 24    39 = 2 + 13 + 24
41 = 4 + 13 + 24    44 = 7 + 13 + 24

So now you have a lovely counterfeit bar as a souvenier. Which, as of today's prices, would be worth about \$18,400 US. Not bad for a day's work.
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