# Monday Maths: Happy Numbers

What is a happy number?  How can a number have emotions?  Can you get sad numbers?  Depressed numbers?  Maybe angry numbers?

Start with any positive integer.  Replace the number with the sum of the squares of its digits.  Keep going, and if you eventually reach 1 then the number is a happy number.

For example 19.

1×1 + 9×9 = 1 + 81 = 82

8×8 + 2×2 = 64 + 4 = 68

6×6 + 8×8 = 36 + 64 = 100

1×1 + 0x0 + 0x0 = 1

So 19 is happy!

There are 143 happy numbers less than or equal to 1000.

What use is this?

As far as I can tell, absolutely none at all.  But it’s kind of fun, don’t you think?  And, if you’re ever stuck on a spaceship with Doctor Who, you might be able to open some of the doors.

A sad number, by the way, is a number which isn’t happy.

An angry number isn’t a mathematical thing, alas, but Angry Numbers is a scrabble-like game for Android phones.

Emotional numbers aren’t a real mathematical thing, either, but they do exist in numerology.  Apparently, the more 2s, 5s, and 8s you have in your birthdate the more emotional you are.  I have all three in my birthdate, and only 2 of the “practical” numbers (1, 4, and 7), which means I should be more emotional than practical. Which is one of the reasons I don’t believe in numerology.

Abundant or Excessive Numbers are numbers where the sum of the proper divisors (all the integer divisors except the actual number) is larger than the number itself.  For example, the divisors of 12 are 1, 2, 3, 4, and 6, which add up to 16, so 12 is an excessive number.

Fibonacci numbers are created by adding the previous two numbers in the sequence:

1, 1, 2, 3, 5, 8, 13, 21, etc

Why not challenge the girls to come up with their own silly name for a set of numbers – and a rule to connect them?