Intermediate Maths Challenge-Style Drill: Counting, Probability and Logic

20 original Intermediate Maths Challenge-style multiple-choice questions on counting, probability and logic, every one written fresh in the style, format and difficulty of the UKMT Intermediate Mathematical Challenge (Year 11 and below), with full worked solutions. This drill targets the topics that quietly decide IMC scores: case-by-case counting with parity (even sums and even products), probability with and without replacement, arrangements with repeated letters and ‘not next to each other’ restrictions, the gap method, pigeonhole arguments, parity invariants, a turn-taking probability game, and knights-and-knaves truth-teller logic puzzles. What’s inside: 6 Easy, 8 Standard and 6 Challenging questions, each with five options A to E and exactly one correct answer, distractors built from the slips students actually make, an IMC-style mark scheme (5 marks for Q1-14, 6 marks for Q15-20 with the real negative marking of -1 and -2) and a one-glance answer grid. Every worked solution breaks the method into short, annotated steps, names the key insight in a ‘Why this works’ note and the trap behind the tempting wrong option, with TikZ tree and seating diagrams where they help, so students learn the competition reasoning rather than just the answer. Ideal for able Year 9 to 11 students preparing for the Intermediate Maths Challenge and the Kangaroo and Olympiad follow-on rounds, for maths clubs and enrichment sessions, and for tutors stretching strong GCSE students towards grade 9. No calculator needed. Original UKMT-style practice material written by Locus Tutors; not produced by, affiliated with or endorsed by the UK Mathematics Trust.