Olympiad Maths Prep

Track / Stage 4 / 184 of 340 #444 of 2000

Problem 444

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer

2. Dr. Q has 5 kittens at home: Big Mi, Second Mi, Third Mi, Fourth Mi, and Fifth Mi. One day, Dr. Q bought each of the kittens a toy: a ball of yarn, a toy fish, a teaser stick, a treadmill, and a mint ball. It is known that:
(1) Third Mi does not like the toy fish and the mint ball;
(2) Fifth Mi does not like the teaser stick and the mint ball;
(3) One of Big Mi and Second Mi gets the toy fish, and the other gets the treadmill;
(4) If Fourth Mi does not get the teaser stick or the treadmill, then Fourth Mi's exercise will be a bit insufficient, and will need to borrow the teaser stick or treadmill from other kittens to exercise;
(5) Second Mi and Third Mi do not share their toys with other kittens.
Given all the conditions, which toy did Big Mi get? ( )
A. Toy Fish
B. Treadmill
C. Teaser Stick
D. Mint Ball
E. Ball of Yarn

Official solution

\begin{tabular}{l}
2 \\
\hline B\mathrm{B}
\end{tabular}

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.