Question

The War of 1812 started with a declaration of war on Thursday, June 18, 1812. The peace treaty to end the war was signed 919 days later, on December 24, 1814. On what day of the week was the treaty signed?

Answer 1

let Thursday be congruent to 0 mod 7

919 days later will be congruent to 919 mod 7 which is equivalent to 2 mod 7

adding two more days to Thursday the answer is saturday

Answer 2

919 days later=919(mod 7)ecause there are 7 days in a week

919(mod 7)=2(mod 7)

2 days after Thursday is saturday

the answer is saturday

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