ikegami,
It's unclear what the OP intended.

Indeed. I updated the root thread to reflect my intentions though I still want people to be able to intepret the puzzle any way they want. These are fun distractions that I like to post and aren't intended to be right or wrong.

Thanks for your contribution. Compare your solution to my by hand solution for a 20 minute target with 3/5/13/19 egg timers.

3    5    13    19
Step1.  3 & 5 together (elapsed time 3 minutes)

3    2/3    13    19
Step2.  3 & 13 together (elapsed time 6 minutes)

3    2/3    3/10    19
Step3.  10 & 19 together (elapsed time 16 minutes)

3    2/3    13    9/10
Step4.  2 & 9 together (elapsed time 18 minutes)

3    5    13    7/12
Step5.  Begin cooking & start 13 (elapsed time 31 minutes)

3    5    13    7/12
Step6.  start 7 (elapsed time 38 minutes)

3    5    13    19
Step7.  Finish cooking 38 - 18 = 20
[download]

Also see where yours fails for 21.

3    5    13    19
Step1 A.  Begin cooking & start 19 (elapsed time 19 minutes)
Step1 B.  Simultaneously start 3 & 5 (no change to elapsed time)

3    2/3    13    19
Step2.  Start 2 (elapsed time 21 minutes)

Step3.  Finish cooking
[download]

Of course, you could run this end to end where the 3/5 is done first to get to the 2 minutes and then start the 19 but that would exceed 21 minutes. I think a nice variation on this puzzle would be to limit the overall amount of time you have to cook the egg. This might force the "setting aside" intermediate timers while longer timers are running.

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