modular-cycle-frequency-count
A sequence (often arithmetic, sometimes a schedule of dates) is distributed across residue bins modulo m, and the problem asks which residue is missing, which bin has the most or fewest, or which histogram matches. The decisive move is recognizing that the period m gives a uniform "base" count over a full cycle and a tail correction over the leftover entries.
How to solve
- Swap modulus 7 (days of week) for modulus 5 (school days) or modulus 12 (months) — the cycle bookkeeping is structurally the same
- Replace 'which histogram matches' with 'which residue never appears' to force the same reasoning without picture options
- Use a non-uniform tail (e.g. last few entries land in a specific cluster) to make the +1 correction step the load-bearing move
Sub-archetype mix (4)
Click a row to see member problems.
- calendar-day-lookup 17% (3)
Given a known starting weekday and a count of days elapsed, determine the resulting weekday by reducing the elapsed count modulo 7 and shifting the starting day accordingly.
- position-in-cycle-lookup 22% (4)
An explicitly-defined repeating object (bin rotation, erased list, iterative rule) partitions items into slots of period P; find which slot holds item N by computing N mod P and tracing the cycle.
- floor-count-across-bins 33% (6)
A sequence of N integers is distributed across m residue bins; compute the base count floor(N/m) shared by every bin, then add 1 to the first (N mod m) bins that receive a tail remainder.
- power-cycle-residue 28% (5)
Find the remainder of a large integer power (or evaluate a polynomial congruence) modulo m by identifying the multiplicative period of the base, then reducing the exponent modulo that period to read off the residue.
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 4 7
- Gr 5 3
- Gr 6 6
- Gr 8 2