Can everyone find a partner?
Odd and Even Numbers
Even numbers pair up perfectly. Odd numbers always leave one out.
-
Step 1 of 5
Try to pair everything up.
Take a pile of counters and put them in twos. If nothing is left over, the number is even. If one is stranded, it is odd.
-
Step 2 of 5
Even numbers split in half exactly.
Sharing between two is the same question as asking whether they pair up. Because they pair up, even numbers can always be shared between two people with nothing left. Odd numbers cannot, without cutting something.
-
Step 3 of 5
The last digit gives it away instantly.
Any number ending in 0, 2, 4, 6 or 8 is even. Ending in 1, 3, 5, 7 or 9 makes it odd. It works for 6 and for 6,483,712 alike.
-
Step 4 of 5
They alternate forever.
Count up and you flip between odd and even every single step, with no exceptions anywhere along the number line.
-
Step 5 of 5
Adding follows neat rules.
Even plus even is even. Odd plus odd is also even — the two lonely ones pair up with each other. Odd plus even is odd.
Computers care a lot about this. Checking whether a number is even is one of the fastest tests a processor can do.
The short version
Pairing is the whole test: what pairs up is even, what strands one is odd, and the last digit settles it for 6 and 6,483,712 alike. It is also why odd plus odd comes out even — the two lonely ones pair up.
Try it yourself
Grab a random handful of coins and pair them up. Before you finish, guess whether one will be left.