Xmas 2018 Puzzle (3)

Seven PLC vendors are selling 1MB memory cards. The respective stocks held by each vendor are:
20, 40, 60, 80, 100, 120 and 140 memory cards.

Each vendor sold all their memory cards at the same lowest price and each received the same amount of money.



What was the price?

Zero.

As in FREE.

They all received zero money.
Poet.

Ha - didn't see that one coming. Take it that the result is actually non-zero.

To sell, "give or hand over (something) in exchange for money", at least that's one definition.
Can you sell something for free?

80?

Phrog30 said:

To sell, "give or hand over (something) in exchange for money", at least that's one definition.
Can you sell something for free?

Click to expand...

Manufacturers mail in rebate

L D[AR2 said:

Seven PLC vendors are selling 1MB memory cards. The respective stocks held by each vendor are:
20, 40, 60, 80, 100, 120 and 140 memory cards.

Each vendor sold all their memory cards at the same lowest price and each received the same amount of money.



What was the price?

Click to expand...

There must be a trick in the wording of the puzzle, because if one vendor sold 20 cards at the same price as the vendor who sold 140, they can't possibly have received the same amount of money, unless the price was zero, which you have ruled out....

No trick in the wording (not like beef cattle and dead chickens). 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..

L D[AR2 said:

No trick in the wording (not like beef cattle and dead chickens). 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..

Click to expand...

L D[AR2 said:

Each vendor sold ALL their memory cards at the SAME lowest price

Click to expand...

To me that seems like a trick in the wording. It could have said that each vendor sold all the cards, and that each vendor sold at the same price. Instead, it says the same price was used for all the cards.

Ok, I checked PG who sell a 1MB memory card for £400.

https://www.parmley-graham.co.uk/au.../s7-400/feprom-memory-card/6es7952-1kk00-0aa0

Let's assume they have the least inventory because of brexit.

So one solution is:
Vendor 1 sold all their memory cards for £8000.
Vendor 2 sold all their memory cards for £8000.
Vendor 3 sold all their memory cards for £8000.
Vendor 4 sold all their memory cards for £8000.
Vendor 5 sold all their memory cards for £8000.
Vendor 6 sold all their memory cards for £8000.
Vendor 7 sold all their memory cards for £8000.

However, we recognise that this means that vendor 7 sold their units at 8000/140 = 54.1428571, which is weird.
If we assume now that:
The same lowest price (in pence) must be divisible by 20, 40, 60, 80, 100, 120, 140.
PGs online prices are not what their customers pay

So.. 8400 is the lowest common multiple of the stock quantities, so the total earnings for each company must be a multiple of £84.00

So one solution is:
Vendor 1 sold all their memory cards for £84.00.
Vendor 2 sold all their memory cards for £84.00.
Vendor 3 sold all their memory cards for £84.00.
Vendor 4 sold all their memory cards for £84.00.
Vendor 5 sold all their memory cards for £84.00.
Vendor 6 sold all their memory cards for £84.00.
Vendor 7 sold all their memory cards for £84.00.

Even the setter of this old puzzle was not happy with the solution, but I thought I would post it anyway.....


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

L D[AR2 said:

No trick in the wording (not like beef cattle and dead chickens). 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..

Click to expand...

But you said "Each vendor sold all their memory cards at the same lowest price"

Clearly they didnt "sell" them all if they were giving some away. and they weren't all sold at the same price if it was "buy the first 10 for x but the rest at y etc."


By your reasoning, the lowest price would have been 0.01, and they gave away all the others for free.....

L D[AR2 said:

Even the setter of this old puzzle was not happy with the solution, but I thought I would post it anyway.....


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

Click to expand...

Even the solution is wrong


Selling 7 for $1 leaves 13 remaining at 3$ each = 7 + (13 * 3) = $46


and 7 at $1 leaving 133 at $3 each is $406

Daba,

Divide Quantity by 7 @ $1 each and Quantity Modulus 7 @ $3 each

20 Divided by 7 = 2 x $1 each) = $2.00, 20 Mod 7 = (6 x $3 each) = $18.00

cwal61 said:

Daba,

Divide Quantity by 7 @ $1 each and Quantity Modulus 7 @ $3 each

20 Divided by 7 = 2 x $1 each) = $2.00, 20 Mod 7 = (6 x $3 each) = $18.00

Click to expand...

But you have only sold 8, not 20 !

L D[AR2 said:

Each vendor sold all their memory cards ....

Click to expand...