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Using HQs, what is the max distance away from a port that you can get at least 1 map supply? Can you chain HQs together? The manual is a bit unclear on how HQs can extend supply so was hoping for some clarification. An example would be if the Axis try to capture Alexandria can they supply it from the Libya ports if they use HQs?

Ports don't really chain...just another supply source.
Distance depends upon a lot of factors...

Ports start at 9 supply.
Roads? On a road supply level will drop 1 so you will get supply out 8 road hexes away, but HQs increase supply by 1.
(So port will be 9, first road out will be 8, next road out will be 7 and so on)
Rail? Supply will be level 9 until rail stops, then drops based upon terrain.
Other terrain take more away from supply...I don't remember each, but I know clear is like a road so 1.

IF the Axis capture Alexandria it is in supply.
Units outside Alexandria if not captured...are to far to be in supply.

Sorry I meant can you chain HQs together? So assuming Allies control Alexandria, how close to Alexandria can you get Axis basic supply using HQs to extend the range?

should be 35, 30 from a port, HQs extend 5. I don't think you can chain them

You can not chain HQs...just one will work.

Ok. So I guess you can essentially get supply 13 hexes away from a port by having a HQ 8 hexes from the port which then extends it another 5. This appears to just reach the hexes adjacent to Alexandria.

All a HQ within 5 of a specific hex does is increase the supply level of that hex by 1. For example, using Tobruk as the supply port, hex 186,10 would be a supply level of zero but if there is a HQ within 5 it becomes a level 1. Similarily hex 185,10 would be a supply level of 1 but the HQ would increase it to 2. So the HQ doesn't actually extend the range, it just increases the supply level of a hex. Have a look at page 57 in the manual and you could also do some hotseat testing.

Actually it does in crease the range because of the 0 level (which means no supply) hexes that will become, for 5 hexes, level 1 instead of 0. Not a huge level of supply, but way better than OOS.

Yep. The only thing I haven't tried yet is moving a HQ more than 8 hexes from a port to see if it would still provide the level 1 supply but my understanding is that it shouldn't.