The NPM collapse of Fiendish 130 is checkpointed, with regular slink marking backup on the solving logic. Then slink marking reveals the more demanding mental task necessary for NPM solving of Fiendish 145.

Your “No Pencil Marks” trace to a collapse of Fiendish 130 could look like this:

If you got stuck, this corresponding regular slink marking will reveal what you missed:

It is longer, isn’t it?  And the point is, we won’t be needing those slink marks.

Turning now to Fiendish 145, the win streak ends. on my first attempt, I managed only four NPM clues. The anemic trace was

NPM: W3, N6, C7, C4

Going back to slink marking, it became evident that I had missed something. Do you see it in the “2:” marking?

When the naked pair 12 closing chute Cc6 is noticed, the NPM trace becomes

A little better, but note, that in this trace, the causes of (C4, C7), SE6, and E8 are hidden. This is not a good feature of a solving trace,  another reason to reject the notion that “no pencil marks” is a superior mode of solving. Pencil marking and tracing the naked pairs, as in dublex bypass tracing, would at least track the state of locked sets and uncommitted cells.

Here is the full result of box marking Fiendish 145. It comes with another strike against NPM. This puzzle requires extensive line marking. Would you want to do it without these pencil marks? Why?

I believe what the NPM solvers would actually do is begin trial and error probing, starting with the naked pair. I hope not. If the answer is more important than the logic leading to the solution, I say just look in the back.

And by the way, in line marking, do line strings count as pencil marks? Do we have to give them up as well, in order to be enlightened?

Outside of the preselected review puzzles, I ran across Fiendish 41, a puzzle that raises an army of naked pairs. For this one, NPM is like blindfold chess.

But the dublex bypass, just by pencil marking the cells locked by the naked pairs, keeps the parade going. From this bypass grid, you can recover the given clues and walk through the trace below to experience this remarkable solving effect. Following the bypass, box marking, line marking and solution are easy.

Bottom line, there is no reason to forgo pencil marks in solving advanced and extreme puzzles. Wayne Gould, and others that claim otherwise can provide no evidence on puzzles not fashioned for NPM. Puzzle publishing is up to its hips in hypoku, and favored labels like “fiendish”, and “no pencil marks” admonitions are equally naive.

Next time, I’ll derive and display the multiple solutions of Fiendish 100. Want to try your own technique first? You have one week.