superprismatic

Of course, TSLF said as much in post #8. So, I can claim no credit here.

True. But naive analysis shows a shortfall. OP asked for blame, or cause, of "apparent" shortfall. That goes to Betty. Kind of. The blame should have had been lain with Betty's mother -- that scalleywag! How about that use of the past pluperfect in conjunction with futuristic pirate talk!

I worked on it for a while until I decided it was just to complex for me to do without writing a program. So, I generated all possible pairs of 9 & 8 long strings which together had 5 lemon, 4 orange, 3 grape, 3 green, and 2 strawberry colors. There are 17!/(5!*4!*3!*3!*2!) = 1,715,313,600 of these. Then, I checked each one of them and counted those which had no same-color skittles touching. There were 1,232,600 like that. That gave me the probability I posted. The program was pretty sloppy but it ran in 69 seconds on one core of my desktop machine.

In order for a pack to contain flavors with those exact proportions, the pack must contain a multiple of 17 Skittles. So, a pack of 20 wouldn't satisfy the hypotheses of the problem!

help me understand this sentence: "Each person receives an anonymous list of 99 numbers representing everyone else's numbers but not her own." it reads to me, that a person would have a list of numbers that excludes the number they have. Let's look at a smaller problem with 10 people and integers between 1 and 10 inclusive. Suppose the 10 numbers given out were 1, 2, 2, 2, 3, 6, 7, 8, 8, and 10. Further suppose that Mary has been assigned the number 2 (not known to her, of course). Then Mary would be given the list 1, 2, 2, 3, 6, 7, 8, 8, and 10. One of the 2s would be missing -- one that represents what she has been assigned. This is the intent of that sentence.

You're correct that puzzles with a similar solution have been on this forum before.

What I was getting at is that 118,400,000 is missing an interpretation in units (in this case, units of length). Any unit of length (including parsecs) would work. So, for example, we could write 118,400,000 m/m3, where the units in the denominator refer to fuel. But writing 118,400,000/m2 doesn't even hint that the numerator should represent distance and the denominator should represent fuel volume. I'll grant you that parsec-m2 is a rather strange unit of volume.

Well, I think that you have to add units to the numerator (as well as the denominator) to make any sense of things. in your example, 25 miles/gal = 118,400,000/m2=118,400,000 parsecs/parsecs-m2. Now that makes physical sense!

I'm not sure how to answer this, but consider that the average of the first 2n integers is (2n+1)/2, not n. It is larger by 1/2.