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Proto

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Discussion starter · #1 · (Edited)
Ok im suscribed to some mathematical and logical riddles discussion list. Ill post some of the most intesting here, enjoy ;)

Ok, first some simple ones, so we can warm up

Some of the Murphy's laws and its derivates are not just pessimist, but in fact have a rational reason. aFind the reason behind these 2 ;)

- When you drop some object, it will always be in the last place you search

-When you dial a number, if its wrong(the number) the line will never be occupated.
 
#2 ·
Quite easy, indeed:

1. It's obvious, since you'll look nowhere else after you find it. Therefore it will be always in the last place you looked.

2. If it were busy you would not know that it's the wrong number.

Keep them coming ;)
 
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Discussion starter · #3 ·
Nice boltz. Ok i found this one a lil interesting

You are the owner of a drogery, and you receive 10 bottles of a medicine. Each bottle has 1000 tablets.

Suddendly, you receive phone call, its your supplier, and he tells you not to sell the medicines, since one of the bottles have tablets that are overcharged with 10mg more of medicine.

You are kinda annoyed by this, since you dont want to lose so much money, so you decide to find out what bottle has the defectous medicine. Since you're also a really lazy bud, you dont want to bother by checking the weight of each bottle in your one-plate weight checker. So you have to find a way to know which bottle has the overcharged tablets with only ONE check.
 
Discussion starter · #4 ·
Ok, this is not really a puzzle but its funny nontheless. Its the Gauss bell applied to real life ^^

Ok here it is. According to our age, our objectives in live can vary dramatically. Here is a rough analisis of them

Our objective at the age of ...:

3 years: not pissing your pants
6 years: To remember what you did during the day
12 years: To have many friends
17 years: Having a driving license
20 years: Having sexual relationships
35 years: Having huge amounts of money
50 years: Having huge amounts of money
65 years: Having sexual relationships
70 years:Having a driving license
75 years: Have many friends
80 years:To remember what you did during the day
85 years: not pissing your pants

:p
 
#6 ·
ProtoMan said:
Nice boltz. Ok i found this one a lil interesting

You are the owner of a drogery, and you receive 10 bottles of a medicine. Each bottle has 1000 tablets.

Suddendly, you receive phone call, its your supplier, and he tells you not to sell the medicines, since one of the bottles have tablets that are overcharged with 10mg more of medicine.

You are kinda annoyed by this, since you dont want to lose so much money, so you decide to find out what bottle has the defectous medicine. Since you're also a really lazy bud, you dont want to bother by checking the weight of each bottle in your one-plate weight checker. So you have to find a way to know which bottle has the overcharged tablets with only ONE check.
Click to expand...
One? Hmm... I could do it in three, but one?

Does it actually involve use of the scale or not?
 
Discussion starter · #7 ·
Does it actually involve use of the scale or not?
Click to expand...
No not really. The problem just picked mg for being a common measure for the dosage in a medicine, but actually it can be anyone. If you want you can use the Proto units, instead of mg :p
 
Discussion starter · #9 · (Edited)
By scale I mean weighing device.
Click to expand...
Aaahhhh.... sorry for that. Blame the language barrier :p

No, it really doesnt matter. Well, you got a one-plate scale but thats all

And well, if you really want the solution here it is, but i encourage you to oslve it by yourself (this means you!!) :p

Lets number the different bottles from 1 to 10. Lets lets put in the scale 1 tablet from bottle 1, 2 tablets from bottle 2 (...) and 10 tablets from bottle 10

If all the bottles had the same concentration on their tablets, we would have 55 weight units of tablets. Since some tablets weight more, we will have a difference here. And by the amount of the difference we can tell which bottle have the defectous tablets. For example if we got a difference of 20mg, we can tell that the bad bottle is number 2, and so on
 
#11 · (Edited)
I think I have it. It requires measuring individual pills as opposed to whole bottles; I assume this is allowed. It also requires knowing the proper weight of the pills.

Basically, I take a distinct number of pills from each of the bottles. By distinct, I mean such that for each bottle, the number of pills you take from that bottle must not be a member of the set of the number of pills you take from each of the other bottles. (Sorry I can't remember the proper set theory term for that. :p )

You place all the pills on the scale, determine the total weight and then use a little bit of algebra.

N = number of pills you placed on scale
W = weight of a good pill
D = difference in weight between a good pill and a bad pill
G = NW (what the total weight of all the pills you placed on the scale would be if they were all good)
T = the total weight of all the pills you placed on the scale

Solve for x:
T = G + (xD).

Whichever bottle you took x pills from is the bad bottle.

For an added bonus, the least amount of whole pills you can use is 45.
 
Discussion starter · #12 ·
Bingo Khan artist. Your solution is even a lil better than the one i found(because i deemd 55 as the minimum)

And you are right, i hadn thoaught about it, but yes, the minimum amount of tablets is 45. If I take 0 tablets from bottle 0, 1 tablet from bottle 1 and so on. If we find that the weight coincides with the theorical one, its because the bottle from which we didnt take any pill is the defectous one.

Hehe... I will post more tomorrow...
 
Discussion starter · #13 · (Edited)
Ok, here is the next one. It is kinda easy anyway, but lets see.

In a sunny day when I was happily resolving some cubic equation, I saw my friend Caroline going out from the music school at 1pm, his father meeted her in that instant and they went in a car to their house. The next day I was around the music school too, and I saw Caroline going out of the liceum at 12:32 pm because a profesor hadnt arrived. She then started walking towards his house, in the same usual path she usually taked with her father. Eventually he found her father, she got in the car and they went to their house, arriving 20 minutes earlier than usual. How many time did Caroline walked?
 
Discussion starter · #16 · (Edited)
Ok... here i got another riddle, although this one is just an extension of an old one. Still kinda fun though

The young prince Alexander went to the Emir of Bagdad to ask for the princess hand, daughter of the paowerful emir Joe XIII. The emir proposed the prince a challenge so that he could demonstrate that he is good enough for his daughter. The challenge consaist on the resolution of the next problem:

I have 5 slaves, the emir said, 2 of them have black eyes, the other 3 have blue eyes. The one that has black eyes always tells the truth, an the blue-eyed ones always lie. In a moment, the 5 slaves will enter the room with their eyes covered. Without seeing their eyes, you have to discover, without the shadow of a doubt, which one is which, and for that you can do 3 questions to 3 of the slaves.

Which are the questions that the prince asked?

And, well, here is th answer for the previous one, but again, I encourage you to find it for yourself

The problem said that they arrived 20 minutes earlier. That means that the car won 10 minutes in its house-school trip and 10 in school-house. This means that he met his daughter at 12:50, So that his daughter walked for 18 minutes
 
#19 ·
The car problem doesn't follow. Here's my argument against your answer.

If she meets her father at the instant she gets out and they drive home, it'll take 10 minutes to get there. that would be 1:10

If she got out early, 12:32, and walked 18 minutes, 12:50, She'd meet her father somewhere, and assuming it'll take her father 10 minutes to get home, 1:00. That would be 10 minutes early, not 20.

Again, that would be assuming it takes her dad 10 minutes, but that's from school to home. It would logically take them even less time to get home due to less distance to cover.

That, or I'm missing something.
 
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Discussion starter · #20 ·
Well... the problem is that we dont really know how much time his father makes from the house to the school, so the best we can do is to call it x/2, and x will be the father's house-school-house trip.

Now, the problem says that they arrived 20 minutes earlier than usual. This means that the fathers trip lasted x-20, this means a gain of 10 minutes go and 10 minutes return for the father

Then we know that Caroline got out earlier and started walking, so that he met his father somewhere in the way, which from the above deduction, we know that this place is 10 minutes far from the school in car, so the hour is 12:50. Which means that Caroline walked for 18 minutes.
 
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