TL;DR; - You get more fault-tolerance with a large number of smaller engines
Either reliability of engines went seriously up, or software control (impossible in early 1960s) made it possible to operate a bunch of less-than-ideal engines successfully.
Due to the lack of funding (the soviet lunar program was given the priority well into the moon "race") they were using the old methodology of testing it in the actual flight, not doing any static fires and only doing a bare minimum of ground testing. Saturn V, on the other hand, heavily relied on the ground testing before the launch. That's why Saturn V mostly worked and N1 failed. Energia worked perfectly much later, because it was developed with the proper amount of ground testing.
Engines alone could be, but the their combination wasn't reliable because of interactions between them and need for synchronization. As Musk points out, it was an avionics problem.
The failure of the N1 program was a leadership issue, period. Just like America trailing the Russians at first was a leadership and lack of focus issue. One team kept winning, then they lost their captains and their funding. Meanwhile, the other team got great leaders and awesome sponsors and started busting their collective ass really hard around the same time - and the wheel of fortune suddenly turned. Funny how that works, isn't it?
What's strange is that the true events sound a heck of a lot more "american" (work hard and reap the laurels, or slack off and be a loser) and yet you keep hearing the same bullshit all the time as to how "the Russian stuff was just inferior". It's not true. And it's not a good story to tell your kids.
Technology turns out to be inferior, when quality control is superseded by political agenda. It should be quite obvious.
See also: https://en.wikipedia.org/wiki/Nedelin_catastrophe
> The failure of the N1 program was a leadership issue, period.
Surely leadership failure is a key factor, but there was also an economical one. Space race was very expensive.
Korolev (pronounce: Karalyov) died in the mid-60s, just before the Moon program had started to gear up for the big time. Khrushchev was ousted also during the mid-60s by retrograde bureaucrats.
With both the political and the technical leadership in turmoil, the program fell on very hard times. The didn't get enough funds, could not get proper testing done, and pushed a lot of QA to the live launches. Predictably, the results were "spectacular" - but in a bad way.
A little before that time America finally got its resolve together ("We choose to go to the Moon in this decade and do the other things, not because they are easy, but because they are hard...") and started pouring massive amounts of financial and engineering efforts into its space program. Again predictably, the results were spectacular - but in a good way.
If your leadership is indifferent and you don't have the stuff you need, you lose. If you work hard and put all your energies into it, you win. And that applied to both sides, each in its turn. Who knew?
Good book on this topic (and related):
https://www.amazon.com/Korolev-Masterminded-Soviet-Drive-Ame...
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I wish Korolev was around these days so he could see Elon Musk's multi-engine design. I think he would like it. In a (somewhat vague) sense, I see the Falcon Heavy as late vindication for the tremendous efforts, against all odds, of the engineers who busted their asses trying to shoot the N1 into the Moon. The idea was sound, it was just not yet the right time for it.
He starts studying liquid fuel rockets in the '30s, and does some amazing work probably trailing only the top German engineers in this field.
He's denounced by some envious low-lifer who wanted his job and is arrested (along with Valentin Glushko, another great rocket scientist) during the stalinist Great Purge at the end of the '30s, when a simple anonymous note was enough to get someone disappeared. They torture him, sentence him to death - but then he's commuted to hard labor in the gold mine, where the poisonous environment and poor conditions meant the average life expectancy was barely over one year. Loses all his teeth to scurvy.
Meanwhile his friends back in Moscow are lobbying with Lavrenti Beria (the KGB boss) to release him - they succeed and he's placed in the "easy prison" where a bunch of intellectuals were doing essentially white collar slave labor (with pencil on paper, sure, but no choice in the nature of the work) for the Soviet government. He's released towards the end of WW2.
Then Stalin figures he needs to catch up to the Germans in rocketry, so Korolev is rehabilitated, made colonel of the Red Army, and finally starts working again on his rocket engines. They copy a bunch of German designs first, use some German engineers (who were prisoners) to get them started. Then continue on their own.
He develops the first Soviet ICBMs, but that was just what paid the bills. He keeps pushing for a real space program. Launches Sputnik 1 into space. Leads the Soviet space program until the mid-60s.
When he died, he was working on plans for manned missions to Mars and beyond.
I mean, what motivates a person to keep forging ahead against such adversity? Death sentence, hard labor in the poison mine, years of imprisonment and disgrace - and then he builds and launches the world's first ever satellite. To say nothing of the fact that, like Elon Musk, he was a man of many talents: great engineer, very effective leader, and a good politician and lobbyist. It's amazing.
It really sounds absurd when put like that. And it makes me wonder what the Soviet space programme could have looked like if Korolev hadn't been imprisoned in Stalin's Great Purge.
The big complication with the N1 was that they tried to steer it with variable thrust, rather than the usual approach of thrust vectoring.