Find concurrent usage durations based on number of systems utilized simultaneously

Would appreciate your help to get a solution
We have 6 desktops in our café for which I have the usage time logged in “Start Time” & “End Time” (without dates, in 24 hr format, goes over midnight 00:00 hrs)

Column A Column B
Start Time End Time
21:37:48 22:47:55
21:37:54 21:59:43
21:53:09 22:10:28
22:10:24 23:30:20
22:17:09 22:57:33
22:49:20 23:24:26
22:57:22 01:42:56
00:23:04 01:12:01
00:23:10 02:16:40
01:12:31 02:18:32
01:44:36 02:21:06
03:15:44 03:32:57
03:27:57 04:47:20
03:29:07 03:53:10

Our requirement is to get the duration for which systems were utilized simultaneously for a day (Evening till next day early morning)

Duration for which 1 system was utilized: ?
Duration for which 2 systems were utilized simultaneously: ?
Duration for which 3 systems were utilized simultaneously: ?
Duration for which 4 systems were utilized simultaneously: ?
Duration for which 5 systems were utilized simultaneously: ?
Duration for which 6 systems were utilized simultaneously: ?

We have been raking our brains for a week now. Would appreciate if you can help us out.

Thanks
Nin

Additional Information:

We have managed to get dates along with the time in following format (this sorts out calculation issue at midnight)
Start Time End Time
20/11/2012 21:37:00 20/11/2012 21:38:00

Thanks

Awesome! This is the first time someone has come up with a solution. VBA is fine with us. The result is not quite what we were looking for. But your solution has resolved it 99% we have now have to add up the duration based on system count.

Thank You!!!

PietBom, thank you for your effort. I appreciate it.

At a glance I thought you had the answer. However I was working entire weekend to modify your logic, but could not. I will give you an example here with easier to understand times as well as its answer.

Time Log & duration
System 1: 20-11-2012 21:00 to 20-11-2012 21:30 - 30 mins
System 2: 20-11-2012 21:05 to 20-11-2012 21:25 - 20 mins
System 3: 20-11-2012 21:10 to 20-11-2012 21:20 - 10 mins
System 4: 20-11-2012 21:15 to 20-11-2012 21:20 - 05 mins
System 5: 20-11-2012 21:20 to 20-11-2012 21:30 - 10 mins
System 6: 20-11-2012 21:20 to 20-11-2012 21:25 - 05 mins

1 system was used: 5 mins
System 1, 20-11-2012 21:00:00 to 20-11-2012 21:04:05

2 systems were used: 10 mins
System 1, 20-11-2012 21:05:00 to 20-11-2012 21:10:00
System 2, 20-11-2012 21:05:00 to 20-11-2012 21:10:00
+
System 1, 20-11-2012 21:25:00 to 20-11-2012 21:30:00
System 5, 20-11-2012 21:25:00 to 20-11-2012 21:30:00

3 systems were used: 5 mins
System 1: 20-11-2012 21:10:00 to 20-11-2012 21:15:00
System 2: 20-11-2012 21:10:00 to 20-11-2012 21:15:00
System 3: 20-11-2012 21:10:00 to 20-11-2012 21:15:00

4 systems were used: 10 mins
System 1: 20-11-2012 21:15:00 to 20-11-2012 21:20:00
System 2: 20-11-2012 21:15:00 to 20-11-2012 21:20:00
System 3: 20-11-2012 21:15:00 to 20-11-2012 21:20:00
System 4: 20-11-2012 21:15:00 to 20-11-2012 21:20:00
+
System 1: 20-11-2012 21:20:00 to 20-11-2012 21:25:00
System 2: 20-11-2012 21:20:00 to 20-11-2012 21:25:00
System 5: 20-11-2012 21:20:00 to 20-11-2012 21:25:00
System 6: 20-11-2012 21:20:00 to 20-11-2012 21:25:00

as you can see off the 30 mins that all 6 systems worked the split for concurrent usage is 1-05 mins, 2-10 mins, 3-05 mins & 4-10 mins

I am working on in but may be you coudl do better

Thanks again

Unable to uploead. Have sent you PM

Excellent PietBom. This is what we are looking for

However, the logic is not working when two "times" are equal.

Eg: if two start times are equal, it takes only one.

You are right PietBom. The calulation was set manual . Thank you once again