Zorac (zorac) wrote,
Zorac
zorac

Number Puzzles

Somethin' to exercise your li'l (sorry) grey cells, a couple of numerical puzzles. First person to solve them both wins 15 seconds of fame.

If A and B can fill a tank in 4 hours, A and C can fill the tank in 5 hours, and B fills twice as fast as C, how long does it take for C to fill the tank alone?
Fairly straightforward, but either the Invariants being slow, or we were all being polite and letting other people have a chance to figure it out...

So, I'm broswing around Sainsbury's, when I see they have large packs of Strongbow (18x440ml cans, normaly £14.99) reduced to half price. Seems like a good offer, but they also have 4-packs at £3.59 each with 500 nectar points if you buy two packs. In addition, these cans have x% extra free, making them a full pint. Question is, which of these offers is better value for money?
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The first one is a five minute calculation if that, a big plus for those who want fifteen seconds (or 0.25 minutes, I suppose) of fame. I'm polite, so I won't spill the beans directly.

The second one is easier. A single four-pack at £3.59 offers the best value for money, as it leaves the most left over to buy Frijj milkshakes which I actually like.
I think you have made a minute error there.

Cider: you can buy 72 440ml tinnies for GBP 29.96 with the first offer, or 72 pint tinnies accompanied by 4500 nectar points for GBP 64.62. We can multiply the 29.96 by 568/440 to get an equivalent volume of cider, so the effective cost of 72 pints of cider with the first offer is GBP 38.67. Therefore you need to find something worth GBP 25.95 to do with your 4500 nectar points in order for the second offer to be better. If you convert nectar points directly into shopping then they're only worth GBP 22.50, which makes the half-price offer slightly better. However, if you can find something more imaginitive to do with 4500 nectar points, then the offer with points becomes better. (Incidentally, you only need to purchase 152 pints of cider, or nineteen gallons of the stuff, to get enough points to go on a scuba-diving course for two. Glug glug!)

Incidentally, this analysis doesn't take into account the normal nectar points you earn from the two purchases, but I doubt they would make much difference.
I shouldn't be at all surprised if there's a minute error in my calculations. I did the math very quickly, even more quickly than the weak steganography. I'm very much playing on your home grounds here. :-)

Going scuba diving after sharing nineteen gallons of Strongbow just seems wrong, somehow. Wasn't there a Public Information Film warning against that kind of thing?
Suppose the vat holds 20 gallons.
A and B are thus filling is at the rate of 5 gallons per hour.
A and C are filling it at 4 gallons per hour.
As B fills twice as fast a C, C must thus be filling at the rate of 1 gallon per hour.
Therefore C alone would take 20 hours to fill it.
Which is, I believe, the answer you first thought of.
Oh good. I'm very mistrustful of my own calculations, especially when mathematicians of jiggery_pokery's kaliber appear to query them. I used a 20 pint pot myself on my piece of rough paper, so I'm glad I was thinking in the right direction for once.

The minute error must therefore have been in the Strongbow/Frijj exchange rate. I guess I overlooked the implied assumption that having lots of Strongbow is considered "good" for the purpose of this question.
'Twas a little gag. I thought you had got the correct answer, 20 hours, already, and had deliberately put "five plus fifteen minutes" instead of "five plus fifteen hours" just for jollity. Minute rather than minute, you see.

If I have to explain it...
<audience-shouts>...it wasn't funny!</audience-shouts>
Oops. That'll be -5 points for UK 'B' instead of the 25 it should have been... attention to detail is obviously a stronger suit for you than for me! If you could just mentally replace "0.25 minutes" with "0.00417 hours" in the previous comment, that would make it work properly. Sound good?
You know, that's so much easier to read when they send you the version of it with HTML as raw text. The <b> tags stand out so easily. ;-)
That pretty much tallies with my mental arithmetic chez Sainsbury. £2.88 is the magic figure for what you need to make your voucher worth, and as a McD's extra value meal now costs more than that, you're sorted.

Of course, another angle of attack is to ignore the extra free on the grounds that is the number of drinks that counts plus you get the bonus of slightly reduced hangovers. In this case you need to get over £5 per voucher, which is pushing your luck some.

The real danger with this sort of scheme is that you count your money twice, eg:
1) I've earned 500 points which is like saving £2.50!
2) I've used a 500 point voucher to save me another £2.50!
A gallon of cider and a McD's extra value meal?

This is your private health insurance company speaking. Your premiums have just nontupled.

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