Cody has a collection of baseball cards.

Question

Cody has a collection of baseball cards. Is it possible for him to place the cards into 5 boxes so that exactly 3 of the boxes contain an odd number of cards and the total number of cards in two boxes is the same as the total number in the other 3 boxes? Explain.

Answer 1

Hi Jordan!  This was a fun one!

 

If exactly 3 boxes have an odd number and two boxes have an even number, then we can name the boxes O1, O2, O3, E4, and E5 (where O means it contains an odd number and E means it contains an even number).

 

Now if we put two boxes together, there is only three ways to do that . . . two odds, two evens, or one of each.

 

If we pair up two odd boxes, their sum must be even.

The three remaining boxes are an odd and two evens.  This sum would be odd - WHICH CAN"T MATCH THE EVEN NUMBER OF THE OTHER TWO BOXES.

 

If we pair up two even boxes, their sum is also even.

The three remaining boxes are the three odd boxes.  Three odd numbers added together is odd - WHICH CAN"T MATCH THE EVEN NUMBER OF THE OTHER TWO BOXES.

 

Last chance!!

If we pair up an odd box and an even box, the sum is odd.

The three remaining boxes are two odds and an even, which add together to make an even number - WHICH CAN"T MATCH THE ODD NUMBER OF THE OTHER TWO BOXES.

 

So, it isn't impossible!  :)

Hope this helps.