TITLE: Programming Logic: - Splitting up Tasks Between Threads
QUESTION [5 upvotes]: I asked this question at stackoverflow and instead of addressing the math required in the problem, they wanted to talk about why setting up 5 threads is no good, or question my intentions. I just want the math solved.
Lets say you want 5 threads to process data simultaneous. Also assume, you have 89 tasks to process.
Off the bat you know 89 / 5 = 17 with a remainder of 4. The best way to split up tasks would be to have  4 (the remainder) threads process 18 (17+1) tasks each and then have 1 (# threads - remainder) thread to process 17. 
This will eliminate the remainder. Just to verify:
Thread 1: Tasks  1-18  (18 tasks)
Thread 2: Tasks 19-36  (18 tasks)
Thread 3: Tasks 37-54  (18 tasks)
Thread 4: Tasks 55-72  (18 tasks)
Thread 5: Tasks 73-89  (17 tasks)

Giving you a total of 89 tasks completed.
I need a way of getting the start and ending range of each thread mathematically/programmability; where the following should print the exact thing I have listed above:
$NumTasks = 89
$NumThreads = 5
$Remainder = $NumTasks % $NumThreads 
$DefaultNumTasksAssigned = floor($NumTasks / $NumThreads)

For $i = 1 To $NumThreads
    if $i <= $Remainder Then
        $NumTasksAssigned = $DefaultNumTasksAssigned + 1
    else
        $NumTasksAssigned = $DefaultNumTasksAssigned
    endif
    $Start = ??????????
    $End = ??????????
    print Thread $i: Tasks $Start-$End ($NumTasksAssigned tasks)
Next

This should also work for any number of $NumTasks. 
Note: Please stick to answering the math at hand and avoid suggesting or assuming the situation.

REPLY [6 votes]: $NumTasks = 89
$NumThreads = 5
$Remainder = $NumTasks % $NumThreads 
$DefaultNumTasksAssigned = floor($NumTasks / $NumThreads)
$End = 0

For $i = 1 To $NumThreads
    if $i <= $Remainder Then
        $NumTasksAssigned = $DefaultNumTasksAssigned + 1
    else
        $NumTasksAssigned = $DefaultNumTasksAssigned
    endif
    $Start = $End + 1
    $End = $End + $NumTasksAssigned
    print Thread $i: Tasks $Start-$End ($NumTasksAssigned tasks)
Next