Remainders and modular cycles

When you divide and something is left over, that leftover repeats on a cycle. If today is Tuesday, then 100 days from now depends only on the remainder of 100 divided by 7. Finding the cycle length and the position inside it answers questions about enormous numbers.

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LearnWhat it is, how to spot it, a worked example, and where it goes wrong.
Practice — 3-point ladder5 problems. Three in a row finishes it.0/3 in a row · 0/5 solved
Practice — 4-point ladder4 problems. Three in a row finishes it.0/3 in a row · 0/4 solved
Practice — 5-point ladder3 problems. Three in a row finishes it.0/3 in a row · 0/3 solved
Skill quizFinish every ladder that has problems first.Finish the ladders above first

Before and after

Needs first

NUM-04Divisibility rules: 2, 3, 4, 5, 9, 10

Opens up

GEO-18Clock geometry: hands, angles, times NUM-07Last-digit behavior of products and powers PAT-03Repeating cycles and position mod n

In official papers

No indexed official paper question has been tagged with NUM-06 yet. The index grows one paper at a time, and it records only question numbers, point values and our own skill tags — never the problems themselves.

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