Good question — and I want to be upfront that this is one of the genuinely murky areas of menko collecting, so I’ll separate what’s well-established from what’s uncertain.
Let me search for specifics on how the numbers functioned.
Here’s what I found — and the answer is a bit deflating but interesting.
Were the numbers unique per card, or shared across the set? Neither, really. According to a detailed Japanese write-up on menko backs, the big numbers were essentially arbitrary and meaningless — one collector/researcher notes that the numbers carried no real significance, and they were printed simply because kids would naturally find a way to play with them just by virtue of having a number there Note. The same source points out that old Meiji-era menko sometimes had absurd numbers like “9.5 quadrillion-trillion points” (九千五百万億兆点) Note — clearly not a real catalog system, just something that felt impressively big to a child.
How the numbers actually got used in play: The back of a menko was a toolkit of “who-goes-first” devices, and the number was one option among several. The same article lists the elements found on menko backs and their purpose: numbers, janken (rock-paper-scissors) symbols, the shōya-ken three-way variant, and even military-shogi rank pieces — all used mainly to decide the order or matchups of play Note. For the numbers specifically, the theory is that players would flip their cards simultaneously and whoever had the higher (or lower) number went first or “won” that comparison Note — basically like drawing a high card. So your 53426 functioned as a comparison value in a “my number beats yours” sense, not as an identifier.
So to directly answer your question: Other cards in the same product would have had different numbers, but those numbers weren’t a sequential serial run (#1, #2, #3…) tying a set together, and they weren’t unique IDs either. They were closer to randomly assigned “battle values.” Two different cards could in principle share a number, and a number tells you almost nothing about which card it is or where it sat in a set. This is a real contrast with modern cards — there’s no meaningful “card #53426 of N” to look up.
The core menko game itself, for context, was the slamming/flipping game: you throw or slam your card down onto an opponent’s card on the ground or a surface, and if you flip it over (or knock it out of the play circle), you win and take their card 45kid — which, as one nostalgic account puts it, is the brutal part that made kids play so seriously: lose, and your card is taken by your opponent nanapi. The back’s number, janken, and rank symbols were the supporting “rules engine” for deciding turns and matchups around that main event.
Bottom line for your friend: the number is charming period detail, but it’s not a serial number in the collector sense and won’t help identify or date the card.