Sum using Multiple criteria over multiple sheets and multiple ranges

Thanks for looking at my post.
I want to add the amount of entries made using a specific number.
I have a log of the start and ending-times each number has been used and in which division (North, East, etc.):
Log.PNG

I also have a log showing the amount of entries each minute. These logs are seperated on 4 worksheets: North, West, South and East. At the end there is a total:
North.PNG

If I want to know how many entries have been made using 10422906, i need to look at which periods 10422906 was used in division North.
Then I look at how many entries were made in that timeframe on the sheet North. There can be multiple timeframes. I need to repeat this for West, South and East. Then I have to total it. I want to leave the division-total as shown in the second image I uploaded out of the calculations.

I've tried al week using sumifs, sumproduct, indirect, array-formulas. I also can't find a similar enough question.
If there is any additional info I can provide, please ask.

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New version

Wow.
This works great. Thanks a million.
My VBA knowledge is too limited to have made this myself. But I have learned a lot by studying your code.

I have tried using this code on my real workbook, but I can't get it to work.
My problems seem to be:
* Sheet Nrs has 97 numbers in column 1. I'd like the sum of entries in column 3. There a total of 8 columns of data.
* Sheet Log has the number in column 8.
* Some numbers in Nrs dont have a entry in Log


John, could you please take a second look or point me in the right direction?

Through trial and error I've gotten the code to work in my real workbook. I've learned a lot. Thank you, John.
I've changed this part of the code to get the sum of the entries in column 3:

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Well done! There is great(er) satisfaction finding the solution by one's own effort.