Xmas 2018 Puzzle (3)

daba · Dec 26, 2018

L D[AR2 said:
The solution is that each vendor charged $1 for 7 memory cards and any left overs were charged at $3 each meaning each vendor received $20 (or whatever units you wish to use)

20 cards = (2 x 1) + (6 x 3) = 20
40 cards = (5 x 1) + (5 x 3) = 20
60 cards = (8 x 1) + (4 x 3) = 20
80 cards = (11x 1) + (3 x 3) = 20
100 cards = (14x 1) + (2 x 3) = 20
120 cards = (17x 1) + (1 x 3) = 20
140 cards = (20x 1) + (0 x 3) = 20

The solution posted would have worked if the stock levels from the 7 vendors were 8, 10, 12, 14, 16, 18, and 20

8 cards = (2 x 1) + (6 x 3) = 20
10 cards = (5 x 1) + (5 x 3) = 20
12 cards = (8 x 1) + (4 x 3) = 20
14 cards = (11 x 1) + (3 x 3) = 20
16 cards = (14 x 1) + (2 x 3) = 20
18 cards = (17 x 1) + (1 x 3) = 20
20 cards = (20 x 1) + (0 x 3) = 20

But I still think the different prices are not in keeping with the wording of the original queston "Each vendor sold all their memory cards at the same lowest price....". The "lowest price" here is $1, and to sell all at that price would nor work.....

alive15 · Dec 26, 2018

They all sold in different currencies, therefore, they all made the same amount of money when converted to one currency.

alive15 · Dec 26, 2018

For example, one vendor sold 20 cards worth $1 each, so made $20 profit, now the guy who sold 40 cards sold in different currency worth 1 (insert correct currency). So he sold received 40 in his currency, which is equal to $20 USD.

cwal61 · Dec 26, 2018

No I sold 20.

2 groups of 7 for $2 (or 14)

and the remaining 6 @ $3 each. For a total of $20

I agree on wording. It's the same pricing method. (not the lowest price)

daba · Dec 26, 2018

"Same pricing method" is a long way off the OP's "same lowest price"...

AustralIan · Dec 27, 2018

I think the real answer is to question ambiguous specifications rather than to assume. You don't always get a customer that knows how to phrase what they want.

In our case, the client came back later and clarified their intent.

What if all the vendors offered the same price but it was for example, buy 10 get one free or buy the first 10 for x but the rest at y etc..

In real life, if someone gives you a clear spec, it is probably because they can code it themselves but they are paid more than you.

mk42 · Dec 27, 2018

Interestingly, I found a forum post discussing some similar problems.

http://mathforum.org/library/drmath/view/61706.html

The conclusion seemed to be that most of the problems were inelegantly worded, preventing the outside the box solutions that were probably intended, leaving only 0 as the result.

5618 · Dec 28, 2018

I’m sure there’s a better answer, but here’s a shot at it. The original post doesn’t explicitly state ALL of each vendor's cards are 1MB. If selling cards at a fixed price per MB, other sizes in the mix can get the same total sales. A possible example:

daba · Dec 29, 2018

5618 said:
I’m sure there’s a better answer, but here’s a shot at it. The original post doesn’t explicitly state ALL of each vendor's cards are 1MB.

Yes it does - "Seven PLC vendors are selling 1MB memory cards."

mk42 · Dec 29, 2018

daba said:
Yes it does - "Seven PLC vendors are selling 1MB memory cards."

Ah, but it doesn't say ONLY 1MB cards. You could say that 7 walmarts sell men's clothes without implying that they don't sell women's clothes.

It's an answer that is entirely silly and against the assumed intentions of the puzzle, but so is OPs solution. If the point is to find wiggle room in the question and think outside the box, it isn't the worst idea.

daba · Dec 29, 2018

mk42 said:
Ah, but it doesn't say ONLY 1MB cards. You could say that 7 walmarts sell men's clothes without implying that they don't sell women's clothes.

It's an answer that is entirely silly and against the assumed intentions of the puzzle, but so is OPs solution. If the point is to find wiggle room in the question and think outside the box, it isn't the worst idea.

If you go back to the original question, it also tells you they sold their entire stock...

Now you have to assume by inference that refers to stock levels of 1MB cards, (a) because that is the only size mentioned, and (b) because you are not told the stock levels of any other size card. Without the assumption that they ONLY have 1MB cards, a solution would be impossible !

EDIT ! I believe I have found a solution ! Just waiting confirmation from the OP....

daba · Dec 29, 2018

My solution to this puzzle doesn't yield a specific price, so the same lowest price has to be $0.01 or £0.01, assuming we go to the lowest unit of currency....

L D[AR2P#0.0] · Dec 29, 2018

Here's the original puzzle, I changed the apples to memory cards

L D[AR2P#0.0] · Dec 29, 2018

and here is the original solution:

daba · Dec 29, 2018

My solution is as follows, and I believe it fulfills all the criteria of the original question....

I figured there had to be a way of balancing out the stock levels, so ....

Vendor 7 sells 20 cards to all the vendors with less stock, so h sells 120 cards, leaves him 20 to sell elsewhere.

Vendor 6 now has 140 cards, he sells 20 to each vendor with less stock, so he sells 100 cards to them, and 40 elsewhere..

This process continues all the way down the chain, and every vendor ends up selling 140 cards, which they can all sell at the lowest same price.

They all receive the same amount of money....

Xmas 2018 Puzzle (3)

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