Library / /151 of 213

, 2015

Combinatorics Difficulty 2.5 Junior Find the answer Canada

Carolyn has a $5 bill, a$ 10 bill, a $20 bill, and a$ 50 bill in her wallet. She closes her eyes and removes one of the four bills from her wallet. What is the probability that the total value of the three bills left in her wallet is greater than $70?

Pick one

Solution

Consider the value of $U$ in the diagram shown.

[[IMAGE0]]

Since a 3 already occurs in the second row, then $U$ cannot equal 3 (each of the numbers $1,2,3,$ occur only once in each row).

Since a 1 already occurs in the third column, then $U$ cannot equal 1 (each of the numbers $1,2,3,$ occur only once in each column).

Since $U$ cannot equal 3 or 1, then $U=2$ .

Therefore, a 2 and a 3 already occur in the second row and so $X=1$ . At this point, a 2 and a 1 already occur in the third column and so $Y=3$ .
The value of $X+Y=1+3=4$ .

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

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