By Math Is Fun, August 29, 2021

After some practice runs of the card game 24, son became very interested and played more. He noticed sometimes the solution is simply adding the values of the 4 cards to get the number 24.

“I can tell if the total of the 4 cards is not 24, in 1 second, without adding the numbers” I told him.

“Tell me how!”

We were staring at the four cards on hand: 5, 6, 3, 9

“The total of the 4 cards is not 24” I said that without much thinking, nor did I do any calculation. “Let me explain. There are two types of numbers: even and odd. If a number can be divided by 2, it’s an even number. If a number cannot be divided by 2, it’s an odd number. Is 1 even or odd?”

“Odd!”

“Right. 1,3, 5… are odd numbers. 2, 4, 6… are even numbers. The property I want you to remember is the following:”

odd number + odd number = even number

odd number + even number = odd number

even number + odd number = odd number

even number + even number = even number

“Out of the four numbers we have, how many odd numbers do we have?”

“3”

“So the sum of these four numbers is an odd number. It cannot be 24, which is an even number. Using the properties of even and odd numbers, if there are either 1 or 3 old numbers from the 4 cards, you can quickly know the sum of the 4 cards is not 24.”

## What do you think?