Question

A man has a job which requires him to work 8 straight days and rest on the ninth day. If he started work on a Monday, the 12th time he rests will be on what day of the week?

• A. Sunday
• B. Wednesday
• C. Tuesday
• D. Friday

Hint:

The rest days fall on day numbers 9, 18, 27, and so on. Find day number 108, the 12th rest, and count that many days after the starting Monday, using the fact that the week repeats every 7 days.

Answer 1

The Correct Option is B

Step 1: Notice how the rest day shifts each cycle.
Each work rest cycle is 9 days long, but the week is only 7 days long. Since $9 = 7 + 2$, every new cycle's rest day lands exactly 2 weekdays later than the previous rest day.

Step 2: Find the first rest day.
He works days 1 to 8 and rests on day 9. Day 1 is Monday, so day 9 is 8 days later, the same weekday as 1 day later since $8 = 7 + 1$, that is, Tuesday. So rest 1 falls on a Tuesday.

Step 3: Step forward 2 weekdays per rest, eleven more times.
Starting from Tuesday and adding 2 weekdays each time for rests 2 through 12: Rest 1, Tuesday. Rest 2, Thursday. Rest 3, Saturday. Rest 4, Monday. Rest 5, Wednesday. Rest 6, Friday. Rest 7, Sunday. Rest 8, Tuesday. Rest 9, Thursday. Rest 10, Saturday. Rest 11, Monday. Rest 12, Wednesday.

Step 4: Check the total shift.
From rest 1 to rest 12 is 11 steps of 2 weekdays each, that is $11 \times 2 = 22$ weekdays. Since $22 = 3 \times 7 + 1$, this is the same as shifting 1 weekday forward from Tuesday, which lands on Wednesday, matching the day by day count above.

Final Answer:
The 12th rest day is a Wednesday.
\[ \boxed{\text{Wednesday}} \]