The Real Explanation of Puzzle 20
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Consider this. If a shop owner sold all of his merchandise, it would be ridiculous to tell him: "You actually made NO profits, because, though you now have all this money, the exact same amount of money in the form of your merchandise is gone! Do you have the merchandise AND the money? No, just the money, which is equatable. So you made no profits at all."
The more in-depth explanation is that we actually can in reality sensibly view merchandise as equal to money, but we have to take into account how much it cost to acquire it before selling it at retail price. This puzzle does not take into account up-marking, which throws everything off and assumes that the shoes were always worth 30, even when the store either bought them wholesale or made them by buying materials. An up-marking example is this. Usually a pair of sneakers is made for, say, $10, and then sold for $80, so the sneakers are NOT worth $80; they are worth $10. The up-mark is $80, NOT the shoes themselves, which are worth, in terms of gain/loss of profits by the person who bought them to sell himself, only $10. So if we take my above example again but include up-marking, the owner can respond "But all of my merchandise was sold at 10 times what I bought it for, so even though the merchandise is gone, I sold it for more, so I now have more."
Think of it like this. In the puzzle, once the fake bill was exchanged, now we are dealing with all real money and shoes. Other members of the board have already written multiple transactions at this point into their explanation, but nothing actually happened within the narrative of this puzzle; the shoes are on the counter not fully bought yet, the clerk is simply going to get change. It's exactly like buying food at a supermarket and the clerk tells you to wait as he goes to another register to get change: you didn't actually buy your food yet, the one transaction is still taking place; everything is on hold. To make it easier you can view the fake 50 as being laundered into a real 50 by the two clerks, and then the first clerk comes back and goes "Okay, let's start the transaction."
So now we have a real 50 given to the clerk, who then sells the shoes, gives change, and completes the transaction. He now has 30 real dollars. If we make the mistake of equating shoes to money and pretend up-marking doesn't exist, then we can say that because his shoes are gone he now has 0 dollars, which makes no sense. The only other way to do the puzzle without up-marking information is to assume he simply made a 30 dollar profit. Doing it this way is the only logically consistent way to do the puzzle with the information provided. If he made actual profit at this point of 30 dollars, then when he reimburses the other clerk for the fake 50, it is 50 minus his 30 in profit from the shoes he sold, which brings his win/loss ratio to negative 20.
The only way you can get to the answer of losing 50 is if you equate the shoes to their retail value, which makes no sense.
Others have also tried approaching this from a strictly accounting perspective rather than a logic puzzle in a game where the primary objective is to look past the distracting transactions
While the cost of the shoes would be the loss in terms of financial reporting, this ignores that the shop owner would consider that he had lost the $30 that he otherwise would've had when the shoes had later been sold (perhaps to the next customer)
... if you equate the shoes to their retail value, which makes no sense
This does make sense unless you're an accountant (who is limited in his view of the world by seeing only the transactions he can record, not what would have been if the shoes had not been stolen)
Someone who worked in retail even agreed with how the puzzle values the shoes (even if the shop's accountant wouldn't) where, for example, retail value is reported for shoplifting purposes
Hershel Layton's Twitter
Okay I'm beginning to see your point. Out of the fake $50, $30 of the fake bill could have been a real $30 had the shoes been properly sold. So while there really is a loss of only $20, the perceived loss of a future shoe sale makes the loss total $50.
Attaching the value of the shoes to a part of the fake $50 seemed to help. I was caught in viewing the shoes as being properly sold — which they were, but not if you consider that the fake $50 is still there and that $30 worth of it could have been REAL money in the future.
If you take away all the misdirection (and that the fake $50 has no value), a woman walks into a store and walks away with $30 worth of shoes and $20 cash without paying
It's reasonable to assign the shoes a value of $30 as that's what they were worth to the clerk, who would've reasonably expected to have sold the shoes for $30
While the (unknown) cost of the shoes (to the store) would've been less, the retail value is what they are worth to the store (based on the information available to the player)
Professor Layton and the Azran Legacy Walkthrough
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