Maths Olympiad Prep

Library / /5 of 520

Combinatorics Difficulty 1.4 Junior Find the answer

Which number in the array below is both the largest in its column and the smallest in its row? (Columns go up and down, rows go right and left.)
\begin{array}[t]{ccccc} 10 & 6 & 4 & 3 & 2 \\ 11 & 7 & 14 & 10 & 8 \\ 8 & 3 & 4 & 5 & 9 \\ 13 & 4 & 15 & 12 & 1 \\ 8 & 2 & 5 & 9 & 3 \end{array}

Pick one

Solution

The largest numbers in the first, second, third, fourth and fifth columns are 13,7,15,12,913,7,15,12,9 respectively. Of these, only 77 is the smallest in its row C\rightarrow \boxed{\text{C}}.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

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