I added this line to the description:

This is a running total, meaning that each count includes the jumps before it. For example [12, 23, 45] means that the child failed 3 times while playing: after the 12th jump, after the 23rd jump, and after the 45th jump.

This problem is poorly phrased. It should state MORE clearly that they take time to fix the rope and RESUME counting the jumps from the number they messed up on, because right now it sounds as though [10,20,30] means the child jumps 10 jumps, messes up, then jumps 20 more jumps the second time, messes up, then jumps 30 times the third time.

confusion from your current phrasing:: The 1st mistake occurred when he jumped 12 times; The 2nd mistake occurred when he jumped 23 times; The 3rd mistake occurred when he jumped 45 times.