h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

A new year was approaching and my old daily trivia desk calendar was nearing an end so I looked for a replacement. I decided to get one that might challenge my mind a bit and I do like puzzles. Well, so far I'm not impressed. One puzzle a few weeks ago listed several 3 digit numbers,
for instance: 171, 513, 342, 285, 627
and then asked for a number that divided into each of these evenly.

OK... fine... I instantly answered 3. The official answer was 57 (in this example, I don't remember the actual numbers). Well, I had to look at the question again and no, it did not stipulate that the answer should be the largest common factor. Oh, well, my answer was just as correct so I went on.

But today's puzzle I think is quite wrong. I didn't even bother trying to find the answer because the question just seemed ignorant. See if you agree or am I indeed wrong and this is a valid question.

I'll paraphrase just a bit to avoid any copyright issues.

You are provided with two petri dishes. Petri dish A has 50,000 bacteria that produce 2500 more per hour. Dish B has 120,000 but 1000 die per hour. How long until both dishes have an equal number of bacteria?

I'll show you the "official" answer and you tell me if I'm correct in deciding to look for a new calendar.

50,000 + 2500x = 120,000 - 1000x
3500x = 70,000
x = 20 therefore they'll have equal populations in 20 hours.

Am I right? Even a overly simple solution would require a bit of calculus (keep in mind, I never took calculus which is why I'm asking this here), wouldn't it?

As more bacteria inhabit dish A, they should produce more bacteria.
More importantly, the problem doesn't state whether they are the same type of bacteria or not, but if you assume that they are, then it seems that there must be some point where the dish becomes overpopulated leading to the reduction of bacteria in dish B.

Anyways, I'm going to go with this answer "They will have equal numbers of bacteria right when I spray them both down with chlorine and rinse them off."

I suppose whoever wrote it also doesn't understand compound intrest.

" I suppose whoever wrote it also doesn't understand compound intrest."

Insert your own satirical joke about the banking system here.

And I agree, the question does display a certain ignorance of how that kind of mathematical system works.

As far as I can make out, the mathematics is correct though the "answer" missed out a step:

50,000 + 2500x = 120,000 - 1000x
so 2500x = 70,000 - 1000x
so 3500x = 70,000
so x = 20

and it is feasible that the bacteria in dish A will die and reproduce to create an absolute increase of 2500 per hour (ie more bacteria mean that more are produced but more die.) It is unlikely but feasible. They may be different types of bacteria that have been growing for different lengths of time so those in dish B have run out of food. *Or* the bacteria in dish B may be allergic to petri dishes and the population is in terminal decline

It isn't fair to add "what ifs?" to a question but I'd get a new calendar nonetheless.

Van

5 12 16 27 41 73.

Which one's the odd one out?

27 its the only one that can be divided by 7
Am i right?

The question doesn't give you enough information to be sure of what rate they grow/die, but you could assume that the rate is proportional to the number of bacteria in the dish (exponential)

I can't be bothered digging out formulae for geometric series, but it's easy to model this on a spreadsheet.

Down column A put the numbers 0 to 20.

In cell B1 put the initial number of bacteria in Dish A (50000)

In cell C1 put the initial number of bacteria in Dish B (120000)

In cell B2 put the formula "=B1*1.05"

In cell C2 put the formula "=C1*119/120"

Drag the formulae in B2 and C2 down those columns until the figure in Column B is greater than that in column C.

This occurs by inspection after 16 hours, when Dish A has 109143 bacteria and Dish B has 104962.

>>5 12 16 27 41 73.

>>Which one's the odd one out?









12
























All the others come with rice.

If you want a shit question - and I'm directly quoting from a local pub quiz that I've not been to since*

"Which animal has no vocal chords?"

....


and the supplementary clue (for those not imagining talking fish)


It's tall.





That's not the only reason I haven't been back but it was amongst the most important ones.

Holy (damnit, somebody antialias that smiley already!)


Here's today's:

75634, 48192, ?, 7320, 1460

What number should replace the question mark?

reductio ad absurdum is a game we can play with many questions:
How do you divide 13 potatoes amongst 7 people? mash them.
How do you resolve the credit crunch? Cancel all outstanding debts.
Easy you see. In fact you missed a trick on the first question you were posed as 1 would have been an equally valid answer, even if it showed a little lack of curiosity.
I agree that the bacteria in question are acting a little strangely, but why not indulge them? 20 was quite an easy answer to get and, even if the question had been sensible I suspect that logs would have sufficed to answer it.
I think I just came down on the side of the calendar, sorry.

The question and answer stated are correct, but they're some seriously strange bacteria.

"Petri dish A has 50,000 bacteria that produce 2500 more per hour. Dish B has 120,000 but 1000 die per hour."

Based on your knowledge of the real world, you're reading stuff into this that isn't actually there. It specifically states a constant rate of growth, so that's what you have to work with, although it wouldn't happen in the real world.

"How long does it take two men to dig half a hole?"

TRiG.

Remember, I paraphrased... I just reread the question and it does NOT assume a constant rate. Here's the actual question (with the original numbers, same answer)

"On petri dish a there are currently 5,000 bacteria that produce another 250 bacteria per hour. On petri dish b there are currently 12,000 bacteria, but 100 die per hour. When will both dishes have an identical bacteria population."


The word 'currently' can be modifying either the current number or the current number and rate. The way it is stated I do assume that the new 250 will also be reproducing at a rate of 0.05 bacteria per hour so in the second hour there may be 262.5 produced and 275.625 in the third hour...

Keep in mind, this is not the first puzzle that I thought to be poorly constructed.

Yeah...psychologically speaking, there's certainly something strange going on - although I'm not quite sure what.

It can be demonstrated experoimentally that children can do sums easier when they involve money rather than abstract sums. It seem easier yo envisage the problem in a concrete domain. (Although very young children seem to get confused when asked to switch from apples to oranges).

You seem to be doing the opposite. The concrete domain seems to be confusing you.

There's a test called the Watson Glaser Test for Critical Reasoning which is meant to test for the ability to separate information from assumptions.

Sorry, Edward, we simulposted. Read the actual wording and see how you would interpret it.

No...you're right to be confused by the bacteria. They'd have been better having, say, a beaker of marbles with a constant number being added every hour. The extra marbles wouldn't themselves multiply.

The missing number is 24159.

It's a cubic polynomial sequence:

f(x) = 3785/6 x³ - 4161/2 x² - 76849/3 x + 102700 (for x = 1,2,3...)

Oddly, the next number in the sequence is 10364 (it starts to increase again).

There answer was 9158. I really do hope your calculations are correct, because your answer makes more sense. I'll hold off on revealing their rational for a bit... it bugs me.

As does my misuse of the word "there" for "their".