# Cracking prices

I recently went to a furniture store where people spend my annual salary on a garish commodes and ostentatious vitrines.

I note a curious code at the bottom of each item’s description label. Some examples:

CP: AUEUC each

SP: FCOSR each

CP: MOES

SP: VUOXS

CP: MLOES

SP: JCSQR

CP: QOND

SP: WSLSF

I assumed CP is Cost Price, and SP is Sale Price. However I didn’t know what to make of the code, I would expect to see repeated letters at the end of the code to represent zeroes, or some other pattern, but there was none of that.

I dared ask the prices of two items and noted they consulted the label before informing me. It took them about a second or so to decode it in their head.

One item was:

CP: MBOZ

SP: XTSP

$650 Another was: CP: XEKTX SP: MOSMV$7500

This is an actual puzzle I've encountered. I do not have a solution.

What puzzling strategies might I use to to crack this pricing code?

• I’d say this is a nice puzzling strategy, I think he just made the “social things” up Mar 27 at 17:32
• It would be good to clarify a couple of things. 1. Whether this is actually a puzzle you've made up with a framing story, or whether the framing story is true and you really are looking for advice on figuring this sort of thing out. 2. Whether the price-codes are all real and accurate, despite the "Something like" when you introduce them. Mar 28 at 1:51
• I'm going to guess that this is in fact a puzzle of Nick's creation, if only because I can't imagine why a shop would record (even in code) the cost prices of furniture on the labels. Mar 28 at 1:53
• @GarethMcCaughan, this is something I genuinely encountered. It does seem odd to be including their cost price, perhaps they have high confidence in their coding. Mar 28 at 2:31
• I have seen a similar thing in 'discount electronic' shops in Singapore (? or maybe Hong Kong - it was a while ago). One 'code' relates to the price to ask first, the second may not be exactly the cost price, but is a guide to the sales clerk for how much the price might drop to if the customer bargains sufficiently. Mar 28 at 22:34

Watch dealers do something similar. They have the sale price in "plaintext", and the money they owe the dealer in a letter code. For the code, they use a secret 10-letter word with no repeating letters, labelling the letters of it 1234567890. E.g. if they use the word BLACKSMITH, MLKH would equal 7250. Source
If we assume this is somehow also the case for this store, we run into the first problem: We know the last given example had a price of \$7500, but both SP and CP has five letters. This can be explained away if we assume the first letter is some kind of meta information. Sometimes this may be a cost/profit ratio or other things. Source Let's test this on the known examples \$650 and \$7500 both have a 5 in them. If they use a secret word, we would have to encounter a duplicate letter in the appropriate positions. And we do on the SPs with the letter S, as long as the first letter indeed is some meta information. (X)TSP 650(M)OSMV 7500 We'll conclude that T=6, S=5, P=0, O=7, M=0, V=0. We'll also conclude that since they told you the value of the SP, the value of CP is less than SP for a given item because CP is the price "they don't want you to know", e.g. cost price or something similar. This hints towards a slightly different approach than the watchmakers. It looks like we have one 9 letter word labelled 1-9, and the rest of the alphabet just represents 0. We can already see that a substring of the secret word has to be STO, since S=5, T=6 and O=7. Unfortunately, it can't be the substring STORE because if E=9, the CP of the last item would start with a 9, making CP > SP, contradicting our assumption. If you somehow still believe me at this point, we can make some deductions We know the secret word is of the form ....sto... Now, we can assume the first (non-meta) letter of each price tag is not 0, otherwise it wouldn't be needed. Let's collect all the first digits of the known examples: UCOLSBTE. So we know the secret word contains all of these 8 letters, and one unknown letter. To further justify this, we can run a frequency analysis of all the given codes. The sample size is small, but nonetheless, you would expect letters that do not represent 0 to occur more often than a specific letter that does represent 0, since there are so many of them. The top 5 results (the ones which occur more often than 2x times) are indeed a subset of UCOLSBTE. It's also noteworthy that it makes sense that S is the most common one, since 5 is arguably the digit which gets used most for prices with no decimal points other than 0. (steps of 50/500, etc) We can make some more deductions with this. We know that CP < SP, and therefore: If both SP and CP of a given item have the same amount of letters, know that the value of the first letter of CP must be less than the value of the first letter of SP, otherwise CP would be higher than SP. E.g. with the first price tag (A)UEUC vs (F)COSR, we can conclude that U < C. Doing this for every item where CP & SP have the same amount of letters, we get the following 4 restrictions: E < OB < TL < CU < C E < O: We know that we have the substring STO taking up 5-7, therefore E must be between 1 and 4 (inclusive) B < T: For the same reason as above, B must be between 1 and 4 L < C && U < C: Both L and U are less than C. Since the lowest values that E and B can have is 1&2, and thereby the lowest values L and U can have is 3&4, we know that C must be either 8 or 9, since 5 is already taken by S. If you're still reading at this point We could already make some good guesses at this point. Nonetheless I ran a quick dictionary search with the given criteria. And indeed, the only sensible combination that matched was BLUE STOCK = BLUESTOCK, giving the following map (all the remaining letters equal to 0): BLUESTOCK123456789 The plainprice map would now be the one shown below. Unfortunately, this is where it all seems to crumble for real-life reasons. Unless the store is extremely over-priced, I don't see how e.g. an item that costs \$8500 has a cost price of \\$2745. That would be insane. My best attempt at explaining myself at this point is that CP is not exactly the cost price, but something similar that's less than SP :) Or maybe the meta-letter has something to do with it...
+------+------+------+| Item |  CP  |  SP  |+------+------+------+|    1 | 3438 | 8750 ||    2 |  745 | 3705 ||    3 | 2745 | 8500 ||    4 |  700 | 5250 ||    5 |  170 |  650 ||    6 | 4960 | 7500 |+------+------+------+