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The Week Counting Problem
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.
| 4 counts | 8 counts | 12 counts | 16 counts |
|---|---|---|---|
| 1w | 1m1w | 2m1w | 3m1w |
| 2w | 1m2w | 2m2w | 3m2w |
| 3w | 1m3w | 2m3w | 3m3w |
| 1m | 2m | 3m | 4m |
| 20 counts | 24 counts | 28 counts | 32 counts |
|---|---|---|---|
| 4m1w | 5m1w | 6m1w | 7m1w |
| 4m2w | 5m2w | 6m2w | 7m2w |
| 4m3w | 5m3w | 6m3w | 7m3w |
| 5m | 6m | 7m | 8m |
| 36 counts | 40 counts | 44 counts | 48 counts | 49 counts |
|---|---|---|---|---|
| 8m1w | 9m1w | 10m1w | 11m1w | |
| 8m2w | 9m2w | 10m2w | 11m2w | |
| 8m3w | 9m3w | 10m3w | 11m3w | |
| 9m | 10m | 11m | 12m | 12m1w |