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EADD Puzzle Corner

BecomingJulie

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Jake the Junkie has just scored 3.2 grams of heroin. He smokes 0.2 g per day. A quarter of whatever he smokes gets deposited on the inside of his tooter where it can later be recovered. How long will his stash last him?

And if it takes a piece of foil 7.5 cm. by 7.5 cm. to make a wrap, 15 cm. by 7.5 cm. to make a tooter and 15 cm. by 15 cm. to make a plate, and he has to make a new plate every time he starts smoking unless he is smoking the inside of a tooter and a new wrap every time he has some gear left at the end of a session, what is the shortest length of foil (on a 30 cm. wide roll) that he will get through?
 
Jake the Junkie has just scored 3.2 grams of heroin. He smokes 0.2 g per day. A quarter of whatever he smokes gets deposited on the inside of his tooter where it can later be recovered. How long will his stash last him?

Nice little red herring in there... 16 days.

And if it takes a piece of foil 7.5 cm. by 7.5 cm. to make a wrap, 15 cm. by 7.5 cm. to make a tooter and 15 cm. by 15 cm. to make a plate, and he has to make a new plate every time he starts smoking unless he is smoking the inside of a tooter and a new wrap every time he has some gear left at the end of a session, what is the shortest length of foil (on a 30 cm. wide roll) that he will get through?

2.4m
 
Last edited:
Nice little red herring in there... 16 days.



2.4m

20 days, the inital stash lasts 16 days but he can recover a quarter of it from tooters so he gets another four days on top of the 16.

There's not enough info to answer the second question.
 
Yep, that's what I worked it out to Owein, the tooters collected 0.8..!

My head hurt to much to carry on with the rest...
 
And if it takes a piece of foil 7.5 cm. by 7.5 cm. to make a wrap, 15 cm. by 7.5 cm. to make a tooter and 15 cm. by 15 cm. to make a plate, and he has to make a new plate every time he starts smoking unless he is smoking the inside of a tooter and a new wrap every time he has some gear left at the end of a session, what is the shortest length of foil (on a 30 cm. wide roll) that he will get through?

To relate the surface integral of the curl of a vector field F over the foil's surface Σ in Euclidean three-space to the line integral of the tooter's inner vector field over its entire boundary ∂Σ:

5f65e93751487f9350c194aa5f2bb8de.png
 
Yeah but it says he smokes 0.2g a day... that's all you need to know. The other statement is not relevant to the question.
 
There's not enough info to answer the second question.
Yes there is. The foil is 30 cm. wide. A 7.5 cm. length is enough to make two tooters, a tooter and two wraps or four wraps. A 15 cm. length will make two plates; a plate and two tooters; a plate, a tooter and two wraps; or a plate and four wraps.

And there's no need for integral calculus -- in fact it's a hindrance, as we are dealing with discrete variables here. If all the halves are confusing you, as intended, temporarily invent a new measuring unit equal to 7.5 cm.
 
hehehe great thread

Jake the Junkie has just scored 3.2 grams of heroin. He smokes 0.2 g per day. A quarter of whatever he smokes gets deposited on the inside of his tooter where it can later be recovered. How long will his stash last him?

And if it takes a piece of foil 7.5 cm. by 7.5 cm. to make a wrap, 15 cm. by 7.5 cm. to make a tooter and 15 cm. by 15 cm. to make a plate, and he has to make a new plate every time he starts smoking unless he is smoking the inside of a tooter and a new wrap every time he has some gear left at the end of a session, what is the shortest length of foil (on a 30 cm. wide roll) that he will get through?

Yeah but it says he smokes 0.2g a day... that's all you need to know. The other statement is not relevant to the question.

It states he "smokes" 0.2g a day; which essentially means he turns the heroin to smoke. The fact that a quarter of the smoke was not collected in his lungs - and has to be re-smoked later - is irrelevant and has caused his stash to be protracted another 4 days.


20 days, 3m of foil.
 
And there's no need for integral calculus -- in fact it's a hindrance, as we are dealing with discrete variables here. If all the halves are confusing you, as intended, temporarily invent a new measuring unit equal to 7.5 cm.

Do you think that's normal? I feel sorry for those whose vector bundles are unit length. I'm keeping it orthonormal.
 
Essentially you can't solve it without arguing over semantics.

If it's 20 days then the calculations for the second part are pretty simple, if it's 16 days not so much.
 
None of you got it right! The answer is 21 days and 172.5 cm. of foil. Here's the explanation:
NSFW:
Day 1, Jake smokes 0.2g. He needs a plate to smoke it from, a tooter and a wrap to restash it afterwards. P=1 T=1 W=1.
Day 2, Jake smokes another 0.2g through yesterday's tooter. He still needs another plate and another wrap. P=2 T=1 W=2.
Day 3, Jake smokes yet another 0.2g. P=3 T=1 W=3
Day 4, Jake smokes yet another 0.2g. P=4 T=1 W=4
Day 5, Jake unrolls the tooter (which now has collected 0.2g.) He only needs to make a new tooter (which will collect 0.05g) to smoke this (no plate, and nothing to restash). P=4 T=2 W=4.
Day 6, Jake smokes 0.2g. from his stash through yesterday's tooter, needing a fresh plate and another wrap. P=5 T=2 W=5.
Day 7, P=6 T=2 W=6.
Day 8, P=7 T=2 W=7.
Day 9, and again there is 0.2g in Jake's tooter. P=7 T=3 W=7.
Day 10, P=8 T=3 W=8.
Day 11, P=9 T=3 W=9.
Day 12, P=10 T=3 W=10.
Day 13, full tooter again, P=10 T=4 W=10.
Day 14, P=11 T=4 W=11.
Day 15, P=12 T=4 W=12.
Day 16, P=13 T=4 W=13.
Day 17, another full tooter. P=13 T=5 W=13.
Day 18, P=14 T=5 W=14.
Day 19, P=15 T=5 W=15.
Day 20, Jake's original stash runs out, so he does not need to make another wrap. P=16 T=5 W=15.
Day 21, and there is still 0.2g. in Jake's (fifth) tooter.

By the end of day 21, Jake has got through sixteen plates, six tooters and fifteen wraps. This can be made from 157.5 cm. of foil, with careful tearing. (120 cm. for 16 plates, 22.5 cm. for 6 tooters and 30 cm. for 16 wraps including one which does not get used.)
 
An Easier One

OK, let's try another one, not so hard this time.

Your boss calls you into his office to give you some bad news. He tells you that business is bad and the company needs to downsize a little. To make it fair, everyone is going to be offered a fair chance to keep their job. He will write "STAY" and "LEAVE" respectively on two identical pieces of paper, swap them about a bit and let you choose one at random. Whatever it says on the paper, that decision is final and binding.

It all sounds fair ..... it's a perfectly even chance ..... However, you notice from the way his pencil moved that he has actually written "LEAVE" on both pieces of paper.

How can you keep your job?
 
None of you got it right! The answer is 21 days and 172.5 cm. of foil. Here's the explanation:
NSFW:
Day 1, Jake smokes 0.2g. He needs a plate to smoke it from, a tooter and a wrap to restash it afterwards. P=1 T=1 W=1.
Day 2, Jake smokes another 0.2g through yesterday's tooter. He still needs another plate and another wrap. P=2 T=1 W=2.
Day 3, Jake smokes yet another 0.2g. P=3 T=1 W=3
Day 4, Jake smokes yet another 0.2g. P=4 T=1 W=4
Day 5, Jake unrolls the tooter (which now has collected 0.2g.) He only needs to make a new tooter (which will collect 0.05g) to smoke this (no plate, and nothing to restash). P=4 T=2 W=4.
Day 6, Jake smokes 0.2g. from his stash through yesterday's tooter, needing a fresh plate and another wrap. P=5 T=2 W=5.
Day 7, P=6 T=2 W=6.
Day 8, P=7 T=2 W=7.
Day 9, and again there is 0.2g in Jake's tooter. P=7 T=3 W=7.
Day 10, P=8 T=3 W=8.
Day 11, P=9 T=3 W=9.
Day 12, P=10 T=3 W=10.
Day 13, full tooter again, P=10 T=4 W=10.
Day 14, P=11 T=4 W=11.
Day 15, P=12 T=4 W=12.
Day 16, P=13 T=4 W=13.
Day 17, another full tooter. P=13 T=5 W=13.
Day 18, P=14 T=5 W=14.
Day 19, P=15 T=5 W=15.
Day 20, Jake's original stash runs out, so he does not need to make another wrap. P=16 T=5 W=15.
Day 21, and there is still 0.2g. in Jake's (fifth) tooter.

By the end of day 21, Jake has got through sixteen plates, six tooters and fifteen wraps. This can be made from 157.5 cm. of foil, with careful tearing. (120 cm. for 16 plates, 22.5 cm. for 6 tooters and 30 cm. for 16 wraps including one which does not get used.)

Nonsense. It's 20 days. I'm way too tired to read through all that and assimilate it; so can you (or someone else) just tell me plainly where you got the extra day from??
 
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