So now it’s clear; the Jean Company is sending the Winfeil Kingdom less coins than it thinks its getting by packing them inefficiently and thereby increasing the number of chests needed to hold them. Their packing method will pass the anti-theft inspection by the Winfeil kingdom, as it only looks to see if any stacks are uneven or layers of coins are missing. They don’t know in what manner the coins are meant to be packed, so they would never notice the inefficiency.

The Winfeil kingdom is being cheated! The question is, how does the Jean Company profit?

Part 2: Profiting from the scheme (first guess)

Later in Volume 8 Lawrence and company eventually end up dealing with the Jean company directly, and the problem becomes less of a riddle and more of a weapon that can potentially be used for leverage in their quest. Because of this, Col reveals the secret and Lawrence then explains how the Jean company can profit from this scheme:

The answer lay in the difference between packing coins in parallel

stacks of similar height or alternating rows.

Either way resulted in a perfectly packed box, such that if any coins

were stolen, it would be immediately obvious.

Moreover, even if there were verbal instructions to “pack coins

tightly in boxes,” the discrepancy would not be noticed, and in any

case, transporting perfectly packed boxes of fixed size reduced the

time spent counting coins, also ensuring that if any coins were taken,

they would be immediately noticed. So at a given time and place, the

only person concerned with how many coins were packed in a box

was the buyer receiving them.

Very clever! The Jean company calculates that if they repack 57 chests of coins using their less-efficient scheme, they can make the coins take up 60 chests instead. This means they only need to order and transport 57 chests in order to fulfill their order. Less chests will mean they save a huge amount of money on taxes and transport costs (which are levied based on the number of chests), which the Jean company can keep as profit:

While in transit, nobody worried about how many coins were in a

box.

This was because taxes were levied by the box, as were

transportation fees.

…

“The Jean Company is probably cutting down on the taxes and

transport costs they pay and turning profit on the excess, but there’s

something very particular necessary for anyone to finally realize that

they are making dishonest gains.”

…

“Yes. Only after we know the details of the export and import can

we begin to suspect foul play. There is far too much volume of trade

in the world to constantly suspect this kind of fraud. One can’t inspect

everything.”

So it seems that the mystery has been solved! As it turns out, they got close but didn’t completely hit on how the Jean company profited from the scheme.

Part 3: Profiting from the scheme (correct answer)

Its revealed that the Jean company is on the verge of bankruptcy. Despite this, it seems as though they intend on purchasing the Narwhal found by local fishermen, and somehow seem to have the capital to do it. Lawrence doesn’t believe that the tax savings they’d make from their repackaging scheme alone would net them the requisite amount to purchase the Narwhal, so how could they do it?

Gold coin substitution idea

At this point in the story, Lawrence is suspected of being in league with Eve to buy the Narwhal and take all the profit that would come from selling it, and she has been captured, interrogated, and is on the verge of being murdered to eliminate her as a risk. With Eve’s life on the line, Lawrence needs to convince her captors that she is not working with the Jean company and, in fact, that company is planning on taking its own action to secure the Narwhal for themselves. Lawrence begins speculating as to how they might acquire the currency to afford it:

“If Reynolds were handling shipments of gold coins…”

“…Using the method Col discovered, he could’ve put aside quite a

lot of capital.”

…

“Taxes are no more than twenty or thirty percent of the value of the

goods. Still, twenty percent of a crate of gold coins is a huge amount

of money.”

Lawrence’s first idea is that if the Jean company might also be handling shipments of gold coins in the same way the handle copper coins. The amount saved per chest on gold coin taxes would be relatively large compared to the amount saved per chest on copper coins. However, since gold coins are more valuable, their chests are more likely to be inspected with greater prudence:

Of course, the coin counts are much stricter for gold, so he

couldn’t have used the same method, I don’t think.”

Scheme reversal idea

Holo then, either thinking aloud or giving Lawrence a hint (unclear here, though she is the Wise Wolf of Yoitsu after all…) provides a clue through a hypothetical question:

“Hmm. The scheme Col noticed — ’twould work better the other

way, I should think.”

…

“Aye,” she answered. “He brings in sixty crates, then sends along fifty-eight. If

he keeps two full crates of copper coins, that’s quite a bit of profit, is it

not?”

For some reason, the book shifts from 57 chests to 58 chests (they also start calling them crates). Weird, but ultimately unimportant. Anyways, Holo seems to be thinking that the Jean company could order the 60 crates asked of them by the Winfiel kingdom from the Debau company, but then take 3 of the crates and repackage the remaining coins to fit the same 60 crates. The coins they’d keep would be the profit.

After that Lawrence seems to reiterate the same idea over again, only this time he explicitly spells out turning 60 efficient chests into 60 inefficient chests, pocketing the coins that wouldn’t fit:

“But that would just amount to breaking even, would it not?”

“Oh? The crates he’d send along would simply contain fewer coins

than the ones he receives down the river, and he’d pocket the

difference. At that rate I’ll bet he could put aside a bit more than twocrates’ worth every time. Of course, in doing so the Debau Company

would take a loss.”

So how would that work? Lawrence wondered to himself.

I’m not really sure where Lawrence’s train of thought was here to be honest, but it’s important because it gets both himself and Col thinking along the right lines. This scheme of taking some coins off the top is good and the Jean company would make lots of money off of it, but we can still do better. After all, if the Debau company has to send 60 chests to the Jean company, they have to pay more in taxes than they would if they only had to send 57 chests.

Final answer

Lawrence and Col then stumble on the correct solution, while Holo watches them quizzically:

“T he absolute number of copper coins won’t change. What changes

is the number of crates, the tax, and…and?” The last word stuck in

Lawrence’s throat out of sheer frustration as he knew he was missing

something obvious. “T he payment! If he can’t reverse the money he’s trading, he just

does it with the payment itself! The Debau Company wouldn’t be

troubled at all! Because — ” “ — If the accounts all balance in the end, there’s no problem. No

problem at all! I wonder what instructions have come downriver to

Reynolds? That would explain why he could have a huge amount of

cash somewhere yet hesitate to use it! That’s it!”

This isn’t actually too big of a change from the original scheme that Lawrence had originally supposed! The Jean Company is still profiting from being able to avoid taxes as before. What Lawrence missed is that the Jean company, in addition to saving on taxes and travel costs, would also keep the money they didn’t spend on those missing 3 chests of copper coins! This would be a not-insignificant amount of money, and with scale would increase the possibility that the Jean company had the money on hand to buy the Narwhal.