geometric-series-share
A self-similar process repeats at a fixed multiplicative ratio: each cycle (or each iteration) shrinks the remaining quantity — share, area, length, count — by the same factor r with |r| < 1. The target quantity is a participant's cumulative share, the total shaded region, or the limiting sum of all stages. Key move: identify the first relevant term a and the per-cycle ratio r, then apply S = a/(1-r) for an unbounded process or S_n = a(1-r^n)/(1-r) for n stages. Often the answer reduces to a clean closed form (e.g. 4/7 of the whole) because the ratio is rational.
How to solve
- Replace 3 sharers (Sarika-Dev-Rajiv) with 4 sharers — first sharer's series becomes 1/2 + 1/32 + ... with r = 1/16
- Change ratio from 1/2 (halving) to 1/3 (third-removal) — first-sharer share drops from 4/7 to 9/26
- Nest squares instead of triangles, with each inscribed square at 1/2 the side — area ratio becomes 1/2 instead of 1/4
Sub-archetype mix (2)
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- nested-similar-figure-area-sum 33% (5)
A figure spawns a similar sub-figure at each step (midpoint triangles, inscribed squares, half-scale copies) and a portion of each new figure is shaded. Areas scale by the square of the linear ratio, giving a geometric series in area. Sum to a/(1-r) (or its finite-stage truncation) for the total shaded area.
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 6 2
- Gr 8 2