#### lpetrich

##### Contributor

Constitution for the United States - We the People specifies the term lengths of its elected officials, and various laws and traditions have filled in the gaps.

- House of Representatives: 2 years
- Senate: 6 years
- President: 4 years

House elections occur on even-numbered years, years with numbers divisible by 2. So on every even-numbered year, the whole House is elected, with the members' terms lasting until the next even-numbered year.

Presidential elections occur on years with numbers divisible by 4. This gives the right term length and it makes a President elected for every two House elections.

Senators could be elected all at once, every 6 years, but the creators of the Constitution decided to stagger the elections of the Senators, making some of the Senators elected each two years, when the Reps are elected. This results in three classes of Senators: Class I, elected on years 6n+2, Class II, elected on years 6n+4, and Class III, elected on years 6n. The three classes are to have numbers of Senators as close as possible to each other, differing by at most 1.

Each state admitted to the Union gets its two states randomly assigned to the three classes, to within that class-size constraint. Let's show how the assignment works with a simple example:

Code:

```
1 2 3
A A A
B AB A B
C AB AC BC
```

It is not known to me what order of Senator assignment the first 13 states had, but Rhode Island (the 13th in) and the rest of the states all fit this pattern.

But if the Senate has an all-at-once election, then the House, the Senate, and the Presidency have elections in a 12-year cycle:

Code:

```
H H H H H H
S S
P P P
```