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There are 45 boxes. Each of them has number on top of it. The numbers are two digit and even. The cups are placed in proportion to half of the number on each of the 45 boxes.
If there is 3645 cups in total. What is the number of cups placed in the highest number written box?

0,34

Mardatonne tefarkardo ihzire hirrime

'The cups are placed in proportion to half of the number on each of the 45 boxes.'
wat

Let's imagine a box which has number 10 on top of it.
Half of it is 5, the cups in the box will be 5k.
If the total cup is 5, then the box will have 5 cups inside.

the number of cups in the box will be 5k*

Wtf

you said there are 3645 cups in total

73.5, so what you cut a cup in half?

You must have done something wrong.

probably, on a work break and have to use iPhone calculator. I know what to do I just probably did it in the wrong order

#5 didn't really help me understand what #4 is confused about (I am confused as well), but I'll throw 147 out there as my answer

Correct!

but 147 is an odd number

What is the number of cups placed in the highest number written box?

#13 (oops)

49

39

69

didn't read but it's obviously 3

147

let me rethink that :)

3645 cups, 45 boxes
3645 / 45 = 81 ... this is the average number of cups needed in a box
since we cannot go over 98 on the box, it cannot all be boxes with "162", so we have to spread it upwards from 81
98 number on box would give use only 49 cups and 49 * 45 is lower than 3645
this has no solution

"The cups are placed in proportion to half of the number on each of the 45 boxes."
This one doesn't mean boxes exactly has half of the number that is written on it.
If half of the number that is written on it is 10, then the cups in it could be 5, 10, 15 etc.
So its 5k, which k is a natural number.
"98 number on box would give use only 49"
It would give us 49k, not exactly 49.

Thanks for explaining, let me try again :)

It's too hard for my weak math skills.
I cam to conclusion, that it is
5k1 + 6k2 + 7k3 + ... + 49k45
where k1..k45 can be between 0 and infinity, only whole positive numbers

no, k's are same. They are all connected.

The amount of cups in a box is three times half of the boxes number.
Highest box number = 98
Amount of cups = 98 / 2 *3 = 147

Correct!

ez math using a PHP script

that was not really stated in the task
if all k's are equal then its 49 *3
Otherwise we can have a lot of solutions

well, you probably miss understood me because of my English level.

but the task is cool tho
Counted while I was walking to the subway
Thx for a good topic

3

10000$

147

What is the point of this when you can't explain it properly? " The cups are placed in proportion to half of the number on each of the 45 boxes." What the fuck does that even mean? I would imagine if box is 10 then cup is 5. But you are saying that it can be 5, 10, 15, so at least say there can be multiplication? I get the 98/2 part but I do not get where the * 3 comes from

a hint
3645 / (5 + 6 + 7 + ... + 49) = 3

10 + 12 + 14... + 96 + 98 = 2430
2430/2 = 1215k
1215k = 3645
therefore k = 3
highest numbered cup = 98
98/2 = 49
therefore 49k is the highest.

Exactly! Just a question, was the translate decent, by decent I mean understandable?

There were a few grammatical errors, however I understood everything just fine!
E.g 'highest number written box' would make more sense if written as 'box with the highest inscribed number'.

Thank you for the suggestion!

Answer is 441
So boxes can have numbers 10, 12, 14, ..., 98
The cups that are placed on them can be 5k, 6k, 7k, ...,49k where k is between 0 and infinity
To achieve max number on a box you need a high k
Divisors of 3645 are 3, 5, 9, 15, 27, 45, 81, 135, 243, 405, ...
Even if all boxes have 5k cups on them it makes 225k cups, so we will only consider the divisor above this number
First consider 243; (try to achive a box with high base cup value, such as 49. But 49 is not possible in this case)
we can achieve this by having 44 boxes with 5k and a box with 23k.
3645/243=15 Then highest number of cups on a box is 23*15=345
Now consider 405;
But this time we can have 49k for one of our boxes. Try to find a combination for other 44 boxes to get 405-49=356
43 boxes with 8k, 1 box with 12k and 1 box with 49k
3645/405=9 Then highest number of cups on a box is 49*9=441
No need for trying other divisors because k value will only drop, and we can't have higher base value than 49

21

"The cups are placed in proportion to half of the number on each of the 45 boxes."
Proportions do not change if you half the numbers.
Total sum of numberss of all the boxes is 10+12+14... + 98 = 54*45 = 2430
So for each number you have 3645 / 2430 = 1.5 cups.
Largest number is 98 so it has 98*1.5 = 147 cups.

Well, if you take wrong path, you pretty much lose time because of that sentence.
Since this question is for an exam and you only have 1.125 minute for a question. It's kinda important.

what are you trying to say?

It confuses some people.

what confuses people?

"The cups are placed in proportion to half of the number on each of the 45 boxes."

Oh, now I get it. That is true.

Btw "k" stands for "kilo" which is 1000. You should use some other symbol for your unkown integers to avoid confusion. Or state that it is some integer.

Yes, thank you!

"in proportion to half of the number on each of the 45 boxes"
it does not says the cups must be in all fucking boxes !!!
stupid english
/closed

it is not that hard you know
you just take the number 3645 / (series of numbers (5,6..49))

Turk English > Czech reading skills.

0/8
number - on each of the 45 boxes
not the cups on or in of each boxes

He was just feeling thank you.

Full focus, fast math

The hardest part about this question was figuring out what was even asked. Thanks #37, No offense but I think I would have understood the question better if Xantares personally explained it to me.

+1

lul

Np.
I'll reword the original question.
There are 45 boxes, each inscribed with a number.
Each number is even, and can only have two digits.
On top of each box, there are a number of pencils, where the quantity of these pencils is declared by half the number inscribed on each particular box.
The total number of pencils is multiplied by an unknown integer, 'k', equalling 3645.
The question: how many cups are on the box with the highest inscribed number.

EZ4ENCE