We are given that 15 boxes contain the total of 100 apples. Prove that there are two boxes with the same number of apples. I'm trying to use PHP, but I'm stuck.
We are given that 15 boxes contain the total of 100 apples
0
$\begingroup$
discrete-mathematics
combinatorial-proofs
2 Answers
5
Hint: You're making your life too hard.
Suppose that all of the boxes do contain different numbers of apples. What is the smallest number of apples you could possibly have?
-
0Your wonderful thank you very much! – 2017-02-07
-
0Very nice hint! – 2017-02-07
0
Suppose $15$ boxes contain different number of apples i.e. say the respective boxes contain $1,2,3,\cdots ,15$ apples in them then the total number of apples required is $120$ but we are only provided with $100$ apples!
If a box contain no apples then largest amount of apple less required is $15$ and then the total number of apples required is $105$ which is still greater than what we are provided with!
-
0A box could contain no apples. – 2017-02-08
-
0see the edit... – 2017-02-08