Track / Stage 1 / 171 of 240 #171 of 2444

Problem 171

Combinatorics Difficulty 1.5 Multiple choice CEMC Pascal · Canada · 2022

Dhruv is older than Bev. Bev is older than Elcim. Elcim is
younger than Andy. Andy is younger than Bev. Bev is younger than Cao.
Who is the third oldest?

Pick one

Official solutions — 2

Solution 1

We use $A$ , $B$ , $C$ , $D$ , and $E$ to represent Andy, Bev, Cao, Dhruv, and
Elcim, respectively.

We use the notation $D>B$ to
represent the fact “Dhruv is older than Bev”.

The five sentences give $D>B$ and
$B>E$ and $A>E$ and $B>A$ and $C>B$ . These show us that Dhruv and Cao
are older than Bev, and Elcim and Andy are younger than Bev.

This means that two people are older than Bev and two people are younger
than Bev, which means that Bev must be the third oldest.

Solution 2

We use $A$ , $B$ , $C$ , $D$ , and $E$ to represent Andy, Bev, Cao, Dhruv, and
Elcim, respectively.

We use the notation $D>B$ to
represent the fact “Dhruv is older than Bev”.

The five sentences give $D>B$ and
$B>E$ and $A>E$ and $B>A$ and $C>B$ . These show us that Dhruv and Cao
are older than Bev, and Elcim and Andy are younger than Bev.

This means that two people are older than Bev and two people are younger
than Bev, which means that Bev must be the third oldest.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.