A removing number problem

11082012, 02:51 PM
Post: #2




RE: A removing number problem
We have to remove $n1$ even numbers $2,4,\ldots,2n2$ so the sum of the remaining is maximum!
The solution is from these Lemma: Lemma1: If we remove $1$ we have to remove $2,3,\ldots$ so we remove all numbers from the set $A$ Lemma2: If we remove $2$, we remove $n1$ numbers $2,4,\ldots,2n2$ so the sum of remaining numbers is $n^2$ Lemma3: If we remove $p$ number $a_1<a_2<a_3<\cdots <a_p$ so we must remove the number $a_1+a_p$ but this number greater than $a_p$ so $a_1+a_p > 2n1 $ A similar way to $a_i$ and $a_{p+1i}$. So the sum of the number which are removed is $\ge n(n1)$ So the sume of the remaining numbers is $< n^2$. 

« Next Oldest  Next Newest »

Messages In This Thread 
A removing number problem  elim  11082012, 02:15 PM
RE: A removing number problem  elim  11082012 02:51 PM
