Library / UKMT Pink Kangaroo /203 of 220

UKMT Pink Kangaroo, 2019

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

A network consists of $16$ vertices and $24$ edges that connect them, as shown. An ant begins at the vertex labelled Start. Every minute, it walks from one vertex to a neighbouring vertex, crawling along a connecting edge. At which of the vertices labelled $P, Q, R, S, T$ can the ant be after $2019$ minutes?

(A) only $P$ , $R$ or $S$ (B) not $Q$ (C) only $Q$ (D) only $T$ (E) all of the vertices are possible

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.