Maths Olympiad Prep

Library / UKMT Junior Kangaroo /219 of 243

UKMT Junior Kangaroo, 2024

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

In how many ways can three kangaroos be placed in three different cells of the grid shown so that no two adjacent cells both contain kangaroos?

(A) 77 (B) 88 (C) 99 (D) 1010 (E) 1111

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.
Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.