Sunday, October 30, 2005

Oh, come ON!

Miriam's teacher has yet to reveal the correct answer to the Rat Population problem (see below), but she did say this: if the first generation is born on day 1 (Jan. 1), the next litter is born 40 days thereafter -- that would be day 41. So far, so good. The next litter is born 40 days after that, but counting begins NOT on day 41 as day 1 of the next cycle, but on day 42, the following day. Thus, the second litter is born not on day 81, the third on 121, etc.; instead, the birth-days for the litters of the first rat couple are 82, 123, 164, etc.

Does this way of interpreting the question seem counter-intuitive for anyone else? Or even flat-out wrong? We're relatively frustrated by the way this interpretation gets rid of the symmetry of the problem, inhibiting the discovery of math formulae to solve it. I insist that Mia's teacher has taken a perfectly interesting math problem and turned it into a stupid busy-work assignment. Math geeks, I need to hear from you.

7 comments:

Bob K said...

What this means is that you have one less iteration than you had before. So I'd say that we were on the right track but just went one step too far.

It strikes me as a difference that the writing of the problem makes hard to discern and the teacher seeing one particular reading of it as definitive smacks of trickery as opposed to mathematics.

Ron Rienstra said...

Yeah, but it's not just a matter of iteration, because the total # of rats after 9 interations is 975; Mia's teacher has told us the correct answer is in the eleven hundreds. See what I mean about the symmetry of the problem being down the toilet?

Phil Smith said...

I agree with Bob, after 9 cycles I get 974 rats. Ron, how do you get an odd number, did you count the teacher? ;-)

Ron, maybe some of the rats get to the tenth cycle and some don't. For example, "newborns" might have babies 120 days later, while the original adults may have babies 123 days later. At the end of the year some would make it to the tenth cycle, and some wouldn't. (You should get back to the teacher and ask if this is a leap year!) By some making it to the 10th cycle and some not, the answer would fall somewhere between 974 and 1808.

I think you could still use my spreadsheet, but you would have to have columns that read "40 days old", "41 days old", etc., and rows for 9 Feb, 10 Feb, 22 Mar, 23 Mar, 24 Mar, etc. How much is this problem worth, anyway?

There is a beauty in a problem that is simple to explain, yet challenging to solve. This is becoming not that kind of problem. It reminds me of the guy in spinal tap, explaining why their knobs all go to 11. Or the old poem that starts "As I was going to St. Ives, I met a man with seven wives..." Or maybe it reminds me of this joke:

Knock Knock.
Who's There?
Control Freak. Now you say, "control freak who?"

Ron Rienstra said...

My bad. 974 is my #.

Further consideration of the grammar also leads me to conclude that our original interpretation of the problem is correct. The key is the word "thereafter." The key question is "after what"? The original birth day, or each subsequent birth day? I would argue the question suggests the former. "Every 40 days thereafter" tells me to count sequences of 40 days after THE FIRST BIRTH-DAY, not a series of 40-day intervals which require a new marker for the "after" starting place. Does that make sense?

Got a huge kick out of the knock knock joke.

Phil Smith said...

The more I thought about this, the more I thought that days 82, 123, etc., don't make sense. If you want to count 40 days after day one, I will grant you that day 41 makes sense. But what if you said "One day later, they had a cheese tasting party." Would that be day 43? Tell Mia that she should hand this in a week late, since when the teacher said "this is due in 1 week" that obviously means 14 days. Sheesh!

I had a high school physics teacher that similarly made no sense from time to time, I had to grit my teeth and remind myself that it will get better. Her mistakes still bug me, though.

Phil

JCR said...

I think Ron's original answer is the correct one - 975. The rest of you forgot to count Karl Rove.

Anonymous said...

I found your blog looking for the answer to the problem recently given to me in school.

I've done the problem myself, and have gotten different answers. I feel confident about it being 1268. But of course I don't know. I will know friday and I can come back and tell you lol.

The way I figure it. The first pair of rats produces 60 rats, thats 62 including themselves.

The First of their litters that is able to produce is on April 28th. (assuming that we start counting from birthdate). That litter (the three females of the 6) produces 18 offspring (9male, 9female).

From there, the 18 offspring can start producing in August. That 18 would produce 54 offspring. There is still one more 120 day period for this 54 to produce once more, so you end up with 162 from that 54. (27 female x 6). This is the ONLY month able to produce 162.

Now you must still take into account that the litter born on January first has yet to produce again, so they produce again in June, July, August, October, November and December. June July and Augsust are able to produce 54. And Oct. Nov. and Dec. cannot produce. So if you multiply the 18 that each litter starts out with by 7 (the number of times the Jan. litter can produce) you get 126.

126+54+54+54+54+162 = 504

This is the total for the original pair's January litter's total offspring.

Then you follow this pattern until you can't anymore.

Feb 9 - Produce 18 on June 6 <-this litter produces 54 on october

Keep this pattern going.

The last month that can produce 54 is august.

All my totals added together gave me 1268.

I'll let you know the actual answer. :]

Yours Truly,

Kyara

aka another person annoyed that they can't find the answer.