Mardatonne tefarkardo ihzire hirrime
'The cups are placed in proportion to half of the number on each of the 45 boxes.'
73.5, so what you cut a cup in half?
didn't read but it's obviously 3
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
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
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.
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
"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.
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.
"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 !!!
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.