This is why I could never stand for election for the society of X or y technique. And even if I was crazy enough to do so, I would certainly never be elected !
You must publically advocate that the technique is wonderful and amazing.
You need the two breaks to be on opposite sides of the stick (since if they are on the same side, one piece will be greater than 1/2, so the other pieces can't match its length).
Probability 1/2
But given that they are on opposite sides, you ALSO need them to be not so far apart that the central segment is >1/2.
I.e., wherever the left break is in the left half, the right break needs to be to the left of within the right half.
This Sam Loyd question is generating lots of very nice equation-based answers, but let me try a method, derived from Zugzwang et al, to see if I can do it without so much algebra, just by thinking.
Suppose we CHANGE the question to this:
"The hour hand and minute hand are SUPERIMPOSED on each other. How long till this superimposition next happens?"
Here is my approach. Suppose it is now just-after-two o'clock. When will this next happen?
First answerer is correct.
And this will continue on in a similar pattern.
When you get to "just-after-11 o'clock", what actually is that time, after 11 o'clock, that the hour and minute hands superimpose?