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Hi All,
I wonder if you can help me with a little puzzle I'm working on. I'll include a picture for clarity. I suspect that you mathsy types will be able to tell me straight away if this is possible or not, but I just can see the obvious...
I have a fine square grid of numbers (blue in the picture), but I do not know the values of the numbers. I also have, overlaid (red in the picture), a more coarsegrained grid of numbers which are the averages of the four numbers they lay ontop of.
I then have another identical large grid (green in the pic) which is displaced by (+1,+1) small grid points. Its values are also the averages of the blue values it obscures.
My question....
If I know all the red and green values (averages of underlying data set), can I work out the blue values? If it can be done, it will no doubt result in a huge string of simultaneous equations. If somebody could start me off by showing how a small section of this could be done, I'd be very grateful. Or if it's impossible, could somebody tell me why?
Would it help to have more large grids offset by other amounts? The grids can extend a long way, and I'm not fussed about knowing ALL the blue numbers  if I can work my way out from the middle, I'll go as far as I need, then forget about the perifery.
Thanks for any help,
Phil
I wonder if you can help me with a little puzzle I'm working on. I'll include a picture for clarity. I suspect that you mathsy types will be able to tell me straight away if this is possible or not, but I just can see the obvious...
I have a fine square grid of numbers (blue in the picture), but I do not know the values of the numbers. I also have, overlaid (red in the picture), a more coarsegrained grid of numbers which are the averages of the four numbers they lay ontop of.
I then have another identical large grid (green in the pic) which is displaced by (+1,+1) small grid points. Its values are also the averages of the blue values it obscures.
My question....
If I know all the red and green values (averages of underlying data set), can I work out the blue values? If it can be done, it will no doubt result in a huge string of simultaneous equations. If somebody could start me off by showing how a small section of this could be done, I'd be very grateful. Or if it's impossible, could somebody tell me why?
Would it help to have more large grids offset by other amounts? The grids can extend a long way, and I'm not fussed about knowing ALL the blue numbers  if I can work my way out from the middle, I'll go as far as I need, then forget about the perifery.
Thanks for any help,
Phil
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