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# Calendar Problem | TOMATO objective 13

Try this beautiful problem from TOMATO Objective no. 13 based on Calendar Problem. This problem is useful for BSc Maths and Stats Entrance Exams.

Problem:

June 10, 1979, was a SUNDAY. Then May 10, 1972, was a

(A) Wednesday;

(B) Friday;

(C) Sunday;

(D) Tuesday;

Solution:

In a (non-leap) year there are 365 days.

$365 \equiv 1 \mod 7$

On a leap year, there are 366 days

$366 \equiv 2 \mod 7$

From 1972 to 1979, there are 7 years (1 of them is leap year). For each non-leap year, we have to go back 1 day and for every leap year, we have to go back 2 days. Hence in total, we have to go back 8 days for those 7 years. Also, May has 31 days. Hence we have to go back 31+8 = 39 days.

Thus $39 \equiv 4 \mod 7$ days before Sunday is a Wednesday.