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Problem 283

Combinatorics Difficulty 1.5 Multiple choice CEMC Gauss (Grade 8) · Canada · 2019

A spinner is divided into 3 equal sections, as shown.

An arrow is attached to the centre of the spinner. The arrow is spun twice. What is the probability that the arrow lands on the same colour twice?

Pick one

Official solution

Barry’s 12 coins include at least one of each of the 5 coins of different values.

The total value of these 5 coins is $\$2.00+ \$1.00+\$0.25+ \$0.10+ \$0.05=\$3.40$ .

Barry has the smallest total amount of money that he could have if each of his remaining $12-5=7$ coins has value $0.05 (the smallest possible value of a coin).

Thus, the smallest total amount of money that Barry could have is $\$3.40+7\times\$0.05=\$3.40+\$0.35=\$3.75.$

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