Maths Olympiad Prep

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CEMC Pascal, 2021

Combinatorics Difficulty 2.3 Junior Find the answer Canada

The two equal-arm scales shown are balanced.

Figure 0

Figure 1

Which of the following has the same mass as

Figure 2

Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Because 2 circles balance 1 triangle and 1 triangle balances 3 squares, then 2 circles balance 3 squares.

Because 2 circles balance 3 squares, then 2+2=42+2=4 circles balance 3+3=63+3=6 squares, which is choice (E).

(Can you argue that none of the other choices is equivalent to 6 squares?)

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