Library / /54 of 149

, 2023

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

There are $66$ cats in my street. I don't like $21$ of them because they catch mice. Of the rest, $32$ have stripes and $27$ have one black ear. The number of cats with both stripes and one black ear is as small as it could possibly be. How many cats have both stripes and one black ear?

(A) $5$ (B) $8$ (C) $11$ (D) $13$ (E) $14$

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.