you’re supposed to find a formula for k for a given n
for example, for n=1, the largest k is 1
also once you figure it out try proving it thbthbthbthbthbt (this is required on the putnam)
HOW IS IT MY FAULT!!!
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tutuu.
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for even n
it is always n/2
(prove is above…)
for odd numbers, I will think on it.
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Oh, N can be put be on itself.
So for odd numbers it would be.
{N} {N-1, 1} … {(n+1)/2 , (n-1)/2}
Making the k max as (n+1/2)
Since N is part of the 1, 2 ,3 … n line, the total sum of any bracket can’t be lower than N, (otherwhise you couldn’t put N in any brackets.)
The same method can’t be used on an even n, since if we start with an {N} bracket and go upwards, we reach eventually an {n/2, n/2} bracket, where we need to use n/2 twice, (which isn’t allowed in the problem) so the lowest sum in an even n case is {n+1}
So my answer, if n is odd k=(n+1)/2
If an is even k=n/2
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i can’t read this have a heart and go
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nyaaaaaaaaaaaa putnam success 
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i am mildly doubtful that i’ll be free today, unfortunately
we’ll see tho
rip
is ok
@May i got a 2.5 liter tub of chocolate ice cream for the equivalent of $3.75. Are you jealous? Please tell me youre jealous. I want you to feel jealous 
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I’m jealous…
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tutuu when any woman
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i am slightly jealous i usually get 2 liters for $4 american dollars
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Goooodddd
Its soooo tastyyyyyy
You want a spoonful? Baby Marluna wants a spoonful? What sound does the air plane make? Fiuuuuuuuu fiuuuuuuu fiuuuuuu
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Shoot me.
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No, thanks.
I’m on a diet. (That’s why I am so jealous.)
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Oh NYOOOOOO wittwe baby ashie we cant play with your water gun now in winter!!! Its cold!!! What if you get a cold? Silly baby ashie oiiiioiiiiioiiiii so small so cute 
. Ashie likes collecting his pokemon? Honkay star rain pokemons? He plays that alll day so cuuteee:blush:. Smol adorable baby
^ ashie when no headpats for 15 minutes. So needy so smol so kyuut
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Not particularly becayse I don’t know its quality
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