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Problem 193

Number theory Difficulty 1.5 Multiple choice CEMC Gauss (Grade 7) · Canada · 2018

Dalia’s birthday is on a Wednesday and Bruce’s birthday is 60 days after Dalia’s. On what day of the week is Bruce’s birthday?

Pick one

Official solution

Since Dalia’s birthday is on a Wednesday, then any exact number of weeks after Dalia’s birthday will also be a Wednesday.

Therefore, exactly 8 weeks after Dalia’s birthday is also a Wednesday.

Since there are 7 days in each week, then $7\times8=56$ days after Dalia’s birthday is a Wednesday.

Since 56 days after Dalia’s birthday is a Wednesday, then 60 days after Dalia’s birthday is a Sunday (since 4 days after Wednesday is Sunday).

Therefore, Bruce’s birthday is on a Sunday.

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