Little explorations with HP calculators (no Prime)

[Albert Chan]

Hi 3298

Sorry I do not follow the logic ... (balls cannot be "rearranged", see post #331)

Actually match_count function (with head + tail version) already proved it.

Inside the loop: s = s - h + t, where h and t = 0 or 1
Thus s is only allowed changes of 0, ±1

s started as sum(head), ended as sum(tail), this implied s visited every integer within the gap.

If gap = 0, sum(head) = sum(tail) = 50, we found the sublist.
If not, 50 is within the gap of visited integers, s must be 50 at some point.