Week 3 Permutations - who needs what

With England completing a clean sweep of home wins on Week 3, it leaves the table looking like this:

Pos	Country	W-L-D	TBPs	LBPs	Pts	Max pts
1	England	3-0-0	1	0	13	23(+3)
2	Ireland	2-1-0	1	1	10	20
3	Scotland	2-1-0	0	1	9	19
4	Wales	1-2-0	0	1	5	15
5	France	1-2-0	0	1	5	15
6	Italy	0-3-0	0	0	0	10

With the remaining fixtures:

Week 4
Friday 10 March: Wales vs Ireland
Saturday 11 March: Italy vs France
Saturday 11 March: England vs Scotland

Week 5
Saturday 18 March: Scotland vs Italy
Saturday 18 March: France vs Wales
Saturday 18 March: Ireland vs England

Italy are the only ones eliminated from title contention after 3 games.

Wales and France are theoretically still in the Championship hunt, but both need two more wins and they're relying on Scotland upsetting England at Twickenham, Italy turning Scotland over at Murrayfield and then Ireland beating England in Dublin. Then it will come down to bonus points, so Wales (having missed a bonus point against Italy) and France (having missed a losing bonus point today) both have ground to make up.

If we can discount the above three teams from the Championship race, we have the following possible permutations.

So here are the scenarios that we can have between the three teams:
Week 4:
Ireland lose, England win - England win Championship in Week 4. By far the simplest permutation to work out. England play for a Grand Slam, Ireland will be trying to play spoiler.

Ireland win, England win - Scotland are eliminated and England and Ireland will play for the Championship in Dublin. An England win is obviously a Grand Slam, but an Ireland win and bonus points, and even points difference, would be crucial.
Possible permutations on above - Ireland can be on 18-20 points, England can be on 17-20 points. My most likely scenario is that there are no try bonus points for either team in the last two weeks, and England take a losing bonus point in Dublin. That puts both teams on 18 and points difference will decide it.

Ireland lose, Scotland win - for simplicity we will assume Scotland beat Italy in Week 5, and Ireland are eliminated form title contention. However, Ireland beating England in Dublin in this scenario would hand Scotland the title. An England win in Dublin would put both England and Scotland on 4 wins, and again bonus points and points difference would be crucial.
Possible permutations on above - Scotland can be on 17-19 points, England can be on 17-20 points. My most likely scenario is that Scotland beat England 4-1 on match-points, Scotland get the try bonus against Italy and England don't take the try bonus point in Dublin. That would put both teams on 18 and again we're looking for points difference.

Ireland win, Scotland win - this puts the 3 front runners on 3 wins each going into the last week. If Scotland were to lose to Italy, Ireland vs England becomes a title decider. Assuming Scotland set the pace with an early win against Italy, Ireland and England will be looking first for the win, but also for a winning equation to overtake Scotland.
Possible permutations on above - Scotland can be on 17-19 points. Were Ireland to win, they could be on 18-20 points. Were England to win they would be on 17-20 points. My most likely scenario is that Scotland beat England 4-1 on match-points and Ireland don't take the try bonus point in Wales. With Scotland getting the try bonus against Italy, that would put Scotland on 18 points and both Ireland and England going into the final game on 14 points, which could then end up being a high-scorer with teams chasing points.

Conclusion
The four games involving one of England, Scotland and Ireland are key.
Wales could play spoiler by beating Ireland in Week 4, but we can probably discount Italy doing the same to Scotland in Week 5.
Scotland are win or bust in Week 4. Anything less than a win against England will see them eliminated. A 4-1 match point win would probably end in a points difference scenario for them. Any bonus point advantage could end up being crucial in the end calculation.
Ireland aren't technically win or bust in Week 4, but if we are talking realistic chances, then yes they are. Failure to take a bonus point against Wales would mean Ireland need to thrash England or rely on points difference. Again, an unexpected try bonus in either of their last two games could be their difference maker.
England could wrap the Championship up with a win in Week 4, if Wales beat Ireland on Friday night. Regardless of the results in Week 4, they'll be in title contention when they run out in Dublin, assuming they avoid a 5-0 match point loss against Scotland.

PS: If England don't take the 5 points from Italy, I'll retype this! But assuming they do, this is what it will look like.

I do not think you will have to retype this. to be honest.

The other matter resulting from the last 2 weeks games is world ranking and in particular who is in the top group of 4 and who drops to below position 8 and so is in the third tranche for seeding purposes come the end of the 6 Nations.

As a result of Scotland beating Wales by more than 15 pts - Scotland and Wales swop places in world rankings (Scotland up to 5th, Wales down to 7th). This now means that Wales and France are in a dodgy position and in the event of Wales losing to Ireland in 2 weeks then Wales v France on the last weekend is a straight shoot out for 9th position for the loser.
If Ireland beat Wales on the 10th March, they are guaranteed a spot in the top 4, if they lose  then Wales can sneak into the top 4 by also beating France, or Scotland can sneak into the top 4 by beating England (they then beat Wales to the top 4 even if Wales win v France). I have presumed that the Italy matches are  wins for France and Scotland for the purposes of these calculations

From a rugby perspective it's a shame that we can so readily discount the probability of Italy winning, but it definitely makes analysis and predictions like these much easier!

If Italy wins any of their matches - well that puts a large spanner in the works - that would mean a 2 ranking pt loss for France or Scotland. However wouldn't really change the outcome regarding RWC seeding - Scotland are safely above Argentina unless Italy beats them by more than 15, and if France lose to Italy then they drop below Argentina but it is still a shoot out with Wales for 8th vs 9th position

Wales need a good kicking