Pigeonhole & Invariants in IOQM: previous year question analysis
Pigeonhole & Invariants has appeared 6 times in IOQM between 2015 and 2025, making it the 14th most-asked of 14 chapters and about 1.7% of the bank. Over the last 5 years it has averaged 1.2 questions per year.
Total PYQs
6
Years covered
2015–2025
Weightage rank
#14 of 14
Share of bank
1.7%
How many Pigeonhole & Invariants questions appeared each year
| Year | Questions | Relative volume |
|---|---|---|
| 2015 | 1 | |
| 2016 | 1 | |
| 2022 | 1 | |
| 2023 | 2 | |
| 2025 | 1 |
Which Pigeonhole & Invariants sub-topics are asked most
Every question in this chapter is tagged to a sub-topic, so you can see exactly where the marks sit before you revise.
- maximum sum-free-type subset via pairing1 questions
- pigeonhole on blocks of consecutive integers1 questions
- extremal combinatorics on a board; guaranteed non-attacking rooks1 questions
- extremal counting / complementary counting (pigeonhole bound)1 questions
- coin-flipping invariant modulo 31 questions
- worst-case guarantee for divisibility by 61 questions
Question formats used in Pigeonhole & Invariants
- Numerical / integer answer6
How Pigeonhole & Invariants compares with nearby chapters
- #12Functional Equations6
- #13Graphs, Games & Sets6
- #14Pigeonhole & Invariants6
Counts are computed from AcadXL’s own IOQM question bank, tagged chapter- and sub-topic-wise and checked against official answer keys. Sign in to attempt the 6 Pigeonhole & Invariants questions with solutions.