Problem 236

[quilan]

So I decided to actually sit down & try and decode what the heck Problem 236 (View Problem) was trying to ask. Unfortunately, after pecking through a few examples I was unable to actually get any meaningful results with the example ratio.

Is it trying to ask the following:
(a,b) = number of Caviar gone bad for 'A' and 'B' respectively.
(c,d) = number of Cake gone bad for 'A' and 'B' respectively.
... (e,f) == Joint, (g,h) == Port, (i,j) = Truffles

Thus, for per-product:
b/640 = m*a/5248
d/1888 = m*c/1312
...

And overall-rate:
(a+c+e+g+i)/18880 = m*(b+d+f+h+j)/15744

I can clear any info from the post (even though I haven't even come close to writing an algorithm for it as I'm still piecing together the word problem) if needed. I just need to know if this an accurate assessment of the initial question for 236?

[ed_r]

I think that's it.

[Lord_Farin]

To the admins:
There is another of those annoying character set problems:
"Although the suppliers try very hard to ship their goods in perfect condition, there is inevitably some spoilage – i.e. products gone bad."

[hk]

Fixed, I hope.

[Lord_Farin]

Yups, nice hyphen there now

[LarryBlake]

Can we assume an integer number of spoiled items? There couldn't be 16/7 spoiled caviar, would there?

[Marcus_Andrews]

Yep -- integers only.

[jinetic]

I somehow ended up with a program that produced 36 possible values of m (as opposed to the expected 35). According to the solution forum, 1107 / 1003 was my extraneous solution; however, I think the following counts for spoiled products satisfy the conditions given in the problem for m = 1107 / 1003:

Supplier A:
0 / 5248
85 / 1312
0 / 2624
2210 / 5760
0 / 3936

Supplier B:
0 / 640
135 / 1888
0 / 3776
1599 / 3766
0 / 5664

Can someone please help me track down my mistake / misunderstanding?

[mpiotte]

there is inevitably some spoilage

each of the five per-product spoilage rates was worse (higher) for 'B' than for 'A'

These quotes from the problem statement exclude solutions with no spoilage for one of more products.

[pjt33]

there is inevitably some spoilage

each of the five per-product spoilage rates was worse (higher) for 'B' than for 'A'

These quotes from the problem statement exclude solutions with no spoilage for one of more products.

I think that is less than crystal clear. It's a perfectly reasonable (and, in general, more natural) interpretation of the first quote that the total number of spoiled items over all products is non-zero. The second quote changes subtly when the rest of the sentence is added, and it appears to be equivalent to the statement that there is an m greater than unity such that each of the five per-product spoilage rates for 'B' is m times the same product's spoilage rate for 'A'.