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I just can't get my head around these topics.

Set up - 3 stands of light infantry are facing 3 stands of heavy infantry that are 1.5 MUs away. The light infantry is offset from the heavy infantry (i.e. if the light infantry moved straight ahead they would not be in front to front and corner to corner contact).

Question 1 - if the 3 stands of light infantry wanted to align, would they use 1 pip of movement to move sideways so that they would be perfectly lined up with the heavy infantry (since they are less than 2 MUs away)?

Question 1a - If the light infantry did align using 1 pip could they then move forward into front contact for combat this turn or would they have to wait until the following turn?

Question 2 - If the 3 stands of light infantry moved straight forward into front to front but not corner to corner contact (because they started offset) would either the light infantry or the heavy infantry slide one way or the other to conform so that there could be combat? If so, is the conforming done before or after contact and which side slides - attacker or defender?

Question 3 - Let's say in the set up above the light infantry were 4 MUs away from the heavy infantry and still offset. My understanding of the rules is that the light infantry couldn't align because they are more than 2 MUs away. Correct?

Question 3a - If the light infantry moved 4 MUs into front to front but not corner to corner contact is there conforming and then combat or just no combat?

Question 4 - Let's say in the set up above the light infantry were aligned to the heavy infantry at an angle - the closest is 1MU from the heavy infantry and the farthest is 2.5 MUs from the heavy infantry. If the light infantry moves as a group straight ahead the closest light infantry unit will contact a heavy infantry unit with its front corner but there will be no edge to edge or corner to corner contact. In this case would the light infantry group stop with no combat? I'm assuming the light infantry that made contact would exert ZOC and that the opposite would be true.

Sorry about the length of the post but I wanted to try to get a bunch of permutations all in one spot.

Set up - 3 stands of light infantry are facing 3 stands of heavy infantry that are 1.5 MUs away. The light infantry is offset from the heavy infantry (i.e. if the light infantry moved straight ahead they would not be in front to front and corner to corner contact).

Question 1 - if the 3 stands of light infantry wanted to align, would they use 1 pip of movement to move sideways so that they would be perfectly lined up with the heavy infantry (since they are less than 2 MUs away)?

You could move each of the 3 individual elements for 1 PIP each sideways, and this would be true even if they were farther away then 2MU.

Question 1a - If the light infantry did align using 1 pip could they then move forward into front contact for combat this turn or would they have to wait until the following turn?

If you choose to use 1 pip per element you could use it to move each individual stand into contact aligning anyway you wish. Combat always happens when stands are in contact, so it happens in the turn they contact.

Question 2 - If the 3 stands of light infantry moved straight forward into front to front but not corner to corner contact (because they started offset) would either the light infantry or the heavy infantry slide one way or the other to conform so that there could be combat? If so, is the conforming done before or after contact and which side slides - attacker or defender?

This would be the most likely way to move the light infantry. The attacking line moves straight ahead and the attacking line slides to conform as long as the slide does not make any of the stands move more than their maximum allowed movement for any of the stands in that line. This is done during movement.

Question 3 - Let's say in the set up above the light infantry were 4 MUs away from the heavy infantry and still offset. My understanding of the rules is that the light infantry couldn't align because they are more than 2 MUs away. Correct?

There is nothing in the rules about being more than 2 MUs away prevents alignment... it comes down to how far they would have to move after the slide. So if after the slide any stand in the moving line would have exceeded its maximum allowed movement measured by the farthest moving front corner, then the slide is not allowed.

Question 3a - If the light infantry moved 4 MUs into front to front but not corner to corner contact is there conforming and then combat or just no combat?

If they have the movement (Light Foot have 5 MU, so it just depends on how far offset they are) then they conform and there will be combat at the end of movement and after any missile fire is resolved.

Question 4 - Let's say in the set up above the light infantry were aligned to the heavy infantry at an angle - the closest is 1MU from the heavy infantry and the farthest is 2.5 MUs from the heavy infantry. If the light infantry moves as a group straight ahead the closest light infantry unit will contact a heavy infantry unit with its front corner but there will be no edge to edge or corner to corner contact. In this case would the light infantry group stop with no combat? I'm assuming the light infantry that made contact would exert ZOC and that the opposite would be true.

The line can wheel into contact as long as no unit exceeds their maximum movement. ZOCs would be exerted if they stopped short of corner to corner contact.