UKMT Senior Kangaroo
99 problems here, rated 1 to 5 on our scale (Junior to AIME, harder). 99 of them ask for a proof. Years covered: 2015–2025.
| # | Topic | Diff | Type | Year | |
|---|---|---|---|---|---|
| 1 | Algebra | 1.0 | proof | 2024 | open |
| 2 | Number theory | 1.0 | proof | 2019 | open |
| 3 | Algebra | 1.0 | proof | 2015 | open |
| 4 | Combinatorics | 1.0 | proof | 2023 | open |
| 5 | Number theory | 1.0 | proof | 2021 | open |
| 6 | Number theory | 1.0 | proof | 2019 | open |
| 7 | Algebra | 1.0 | proof | 2025 | open |
| 8 | Geometry | 1.0 | proof | 2016 | open |
| 9 | Geometry | 1.0 | proof | 2016 | open |
| 10 | Number theory | 1.0 | proof | 2023 | open |
| 11 | Number theory | 1.0 | proof | 2021 | open |
| 12 | Number theory | 1.0 | proof | 2023 | open |
| 13 | Number theory | 1.0 | proof | 2016 | open |
| 14 | Algebra | 1.0 | proof | 2015 | open |
| 15 | Algebra | 1.0 | proof | 2024 | open |
| 16 | Number theory | 2.0 | proof | 2016 | open |
| 17 | Combinatorics | 2.0 | proof | 2024 | open |
| 18 | Algebra | 2.0 | proof | 2019 | open |
| 19 | Number theory | 2.0 | proof | 2021 | open |
| 20 | Algebra | 2.0 | proof | 2023 | open |
| 21 | Algebra | 2.0 | proof | 2016 | open |
| 22 | Algebra | 2.0 | proof | 2023 | open |
| 23 | Algebra | 2.0 | proof | 2018 | open |
| 24 | Combinatorics | 2.0 | proof | 2025 | open |
| 25 | Algebra | 2.0 | proof | 2016 | open |
| 26 | Algebra | 2.0 | proof | 2016 | open |
| 27 | Algebra | 2.0 | proof | 2024 | open |
| 28 | Combinatorics | 2.0 | proof | 2017 | open |
| 29 | Algebra | 2.0 | proof | 2024 | open |
| 30 | Algebra | 2.0 | proof | 2018 | open |
| 31 | Algebra | 2.0 | proof | 2015 | open |
| 32 | Combinatorics | 2.0 | proof | 2024 | open |
| 33 | Number theory | 2.0 | proof | 2018 | open |
| 34 | Algebra | 2.0 | proof | 2019 | open |
| 35 | Geometry | 2.0 | proof | 2016 | open |
| 36 | Number theory | 2.0 | proof | 2023 | open |
| 37 | Number theory | 2.0 | proof | 2023 | open |
| 38 | Algebra | 2.0 | proof | 2016 | open |
| 39 | Combinatorics | 2.0 | proof | 2023 | open |
| 40 | Number theory | 2.0 | proof | 2024 | open |
| 41 | Algebra | 2.0 | proof | 2019 | open |
| 42 | Algebra | 2.0 | proof | 2023 | open |
| 43 | Number theory | 2.0 | proof | 2025 | open |
| 44 | Number theory | 2.0 | proof | 2017 | open |
| 45 | Geometry | 3.0 | proof | 2021 | open |
| 46 | Algebra | 3.0 | proof | 2015 | open |
| 47 | Number theory | 3.0 | proof | 2021 | open |
| 48 | Number theory | 3.0 | proof | 2019 | open |
| 49 | Number theory | 3.0 | proof | 2017 | open |
| 50 | Algebra | 3.0 | proof | 2019 | open |
| 51 | Combinatorics | 3.0 | proof | 2015 | open |
| 52 | Combinatorics | 3.0 | proof | 2023 | open |
| 53 | Number theory | 3.0 | proof | 2023 | open |
| 54 | Number theory | 3.0 | proof | 2017 | open |
| 55 | Number theory | 3.0 | proof | 2017 | open |
| 56 | Algebra | 3.0 | proof | 2015 | open |
| 57 | Number theory | 3.0 | proof | 2017 | open |
| 58 | Number theory | 3.0 | proof | 2016 | open |
| 59 | Number theory | 3.0 | proof | 2018 | open |
| 60 | Combinatorics | 3.0 | proof | 2021 | open |
| 61 | Geometry | 3.0 | proof | 2023 | open |
| 62 | Geometry | 3.0 | proof | 2017 | open |
| 63 | Combinatorics | 3.0 | proof | 2024 | open |
| 64 | Number theory | 3.0 | proof | 2025 | open |
| 65 | Number theory | 3.0 | proof | 2015 | open |
| 66 | Number theory | 3.0 | proof | 2016 | open |
| 67 | Combinatorics | 3.0 | proof | 2023 | open |
| 68 | Algebra | 3.0 | proof | 2025 | open |
| 69 | Geometry | 3.0 | proof | 2017 | open |
| 70 | Combinatorics | 3.0 | proof | 2015 | open |
| 71 | Algebra | 3.0 | proof | 2025 | open |
| 72 | Combinatorics | 3.0 | proof | 2015 | open |
| 73 | Combinatorics | 3.0 | proof | 2016 | open |
| 74 | Combinatorics | 3.0 | proof | 2023 | open |
| 75 | Number theory | 3.0 | proof | 2019 | open |
| 76 | Algebra | 3.0 | proof | 2019 | open |
| 77 | Number theory | 3.0 | proof | 2016 | open |
| 78 | Algebra | 3.0 | proof | 2018 | open |
| 79 | Geometry | 3.0 | proof | 2018 | open |
| 80 | Combinatorics | 3.0 | proof | 2016 | open |
| 81 | Number theory | 3.0 | proof | 2025 | open |
| 82 | Algebra | 3.0 | proof | 2015 | open |
| 83 | Number theory | 3.0 | proof | 2025 | open |
| 84 | Number theory | 3.0 | proof | 2023 | open |
| 85 | Combinatorics | 3.0 | proof | 2024 | open |
| 86 | Algebra | 3.0 | proof | 2018 | open |
| 87 | Number theory | 3.0 | proof | 2019 | open |
| 88 | Number theory | 3.0 | proof | 2019 | open |
| 89 | Algebra | 3.0 | proof | 2018 | open |
| 90 | Combinatorics | 3.0 | proof | 2021 | open |
| 91 | Algebra | 3.0 | proof | 2021 | open |
| 92 | Number theory | 5.0 | proof | 2024 | open |
| 93 | Combinatorics | 5.0 | proof | 2018 | open |
| 94 | Number theory | 5.0 | proof | 2015 | open |
| 95 | Combinatorics | 5.0 | proof | 2025 | open |
| 96 | Number theory | 5.0 | proof | 2018 | open |
| 97 | Geometry | 5.0 | proof | 2019 | open |
| 98 | Number theory | 5.0 | proof | 2017 | open |
| 99 | Geometry | 5.0 | proof | 2021 | open |
These are sorted by difficulty within the competition, but they aren't a course.
The track is the route through, drawn from all the sources at once.