There are three family member groups each containing three digits.

We have already seen one of these family groups and that was the 3 times table.

3 6 9

This sequence is a key to unlocking the other two groups, when we were looking at the the 3 times table we started the sequence with a 3, well we can count in 3s but instead of starting with a 3 lets start with a 1 then we will constantly keep adding 3 to the total

**Three Times Table (adding 3) Starting With a 1**

1 4 7

If we continue by 7 + 3 = 10 would implode back to a 1 so it would repeat, so now we have our second family member group and that leaves three digits left to make up the final group. Lets start a new sequence using the same method of adding 3 but this time we start with a 2.

**Three Times Table (adding 3) Starting With a 2**

2 5 8

That completes the set and all female digits have been used.

Just for completeness lets have a quick look at the 6 times table, we will create three sequences of numbers starting with a 1 a 2 and a 3 each time adding 6 and we get.

1 7 4

2 8 5

3 9 6

If we implode the digits in a family group get

1 4 7 >)3 so I will be referring to this group as the 3 family group (even though the 3 is not in this group)

2 5 8 >)6 so I will be referring to this group as the 6 family group (even though the 6 is not in this group)

3 6 9 >)9 so I will be referring to this group as the 9 family group.

Notice that the nine family group is the only group that contains a polar pair, the 3 and the 6, also this group contains the almighty 9 as such this group is complete and is different to the other two groups. The 3 and 6 family groups are two halves that make up one whole. A closer look at how these family groups interact should explain what I mean.

**1 4 7 and 1 4 7**

Notice that when any instance of the 3 family group interacts with any other instance of the same group the result is one of the 6 family member group

3+3>)6

**2 5 8 and 2 5 8**

Notice that when any instance of the 6 family group interacts with any other instance of the same group the result is one of the 3 family member group.

6+6>)3

**1 4 7 and 2 5 8**

When member of the 3 and 6 family groups interact the 9 family group is created.

3+6>)9

**1 4 7 and 3 6 9 | 2 5 8 and 3 6 9 | 3 6 9 and 3 6 9**

Now if any family member group interacts with the 9 group the same group is created.

This is just like adding any single digit to 9 the same digit is created.

3+9>)3

6+9>)6

9+9>)9

So as you see the members of each group act just like their female number.

We will be looking at family groups in all the following sequences but before we move on, lets have a look at the family members in our times tables

Note that in all times tables and in all family groups each member in each group are perfectly equal distance apart.

Here is something I find interesting and a easy way to remember what digits belong in which family group.

There is a good reason why if one family member group is the right way up then the other must be upside down and that we will see in the next part.