[McLeopold]

Let's assume the shepherd graduated high school at 18 then bought 2 lambs and a farm. He was nice to his sheep so didn't breed them until 2 years and not after 7. The average litter size is 2 and the average age is 11. Let's assume an even number of male and female sheep. At year 2 he'll have 4 sheep (2 original and 2 new lambs). 2 more at year 3 and then 4 at year 3 (the first litter can now breed). At year 7 the original sheep stop breeding.

The shepherd is about 30 years old after he has passed the 125 mark. The dogs didn't matter. (Some story problems throw you a red herring.)

[will_work4tears]

Or, conversely, the shepherd is 16 and they are the father's sheep. Nobody said they were his sheep.

[McLeopold]

You're right, nobody did say that. The point I was trying to make is that with the absence of data, you have to make assumptions and they should be clearly defined. My assumptions defined his starting age and how he obtained the first 2 sheep and the fact they were his.

I guess I would want my kids too look at any math problem with the following things in mind: * identify units of measurement * identify useful data * identify non-useful data * identify assumptions needed to complete answer

There are more or different assumptions I could make, such as cooperative breeding amoungst other breeders or a larger flock to start with, or a completely different model of breeding sheep. I could have described a scenario where he started with 2 sheep and went through several trading and auction rounds until he had 125 with some bonus dogs like the guy that got a house from a paper clip.

We don't have a time measurement in years, so we need some type of sheep per time or time per sheep unit. I choose an assumption of breeding and came up with about 1 sheep per year per sheep.

The original question is very close to a nonsense question, which requires so many assumptions that probably most answers can be well defended with the right set of assumptions. But at the very least you would hope a student could identify an answer in years could not be obtained with the given data of # of sheep and # of dogs.

(And, no, I don't think the units method is beyond an eight grader, even if the educational system thinks it is. The fermi problem may be.)

[jessaustin]

A certain amount of inbreeding of livestock is OK, but your hypothetical shepherd is asking for problems. b^)