On a discord I frequent, there are many channels and threads devoted to kinds of counting. One channel is simply adding 1, like normal counting. There are counting by 5s, 10s, 100s, 1000s. There is a section where the community can add sillier counting (or chaining) methods, and threads have been created which simply alternate 6 and 7, just saying “e”, using a random single emoji one after another, spelling out QUACK but alternating 1 letter & 2 letters at a time (Q, UA, C, KQ, U, AC, K, etc).

One such silly thread I devised, is counting by weeks, beginning with 1 week. After 3 weeks comes 1 month, and after 12 months 3 weeks comes 1 year. However, one user pointed out that from 1 week thru 1 year is actually only 48 counts, instead of 52 counts for 52 weeks of the year. Even if we complete the cycle to 1 year 1 week, since we started with 1 week and not 0-anything, that still only comes to 49 counts. If we did retro-insert an implied 0-week, that would still make only 50 counts. How do we account for the missing ones shy of 52?

1. Need we bother, with ensuring each year comes up to 52 counts (since counts are not tallied in the actual process), and just leave it at the incompleteness of 52? The simple answer to that is no, and to just move on.

2. If do need bother, what solution should we apply, to ensure each of the 52 weeks is accounted for, but without interrupting the normal flow of the process?

Let's explore adding 1 leap weeks every 6 months: insert a 6m0w leap-week every 6 months, as a separate count from the normal 6m, so that we go 5m2w, 5m3w, 6m, 6m0w, 6m1w, 6m2w. That would show up as:

This seems like a viable solution, but wouldn't that therefore make the start of the next count of 1y2w be the starting count for the next 52, whereas the start of the first 52 was 0m0w?