1. Robinson Crusoe replenishes his supply of drinking water from a source every second day, gathers fruits every third day, and goes hunting every fifth day. Today, September 13, is a tough day for Robinson: he has to do all three of these tasks. When will Robinson have his next tough day?
Answer: October 13.

## Solution.

We will count how many days have passed since the "heavy" day. If this number is divisible by 2, then Robinson needs to replenish his water supply. If it is divisible by 3, then he needs to replenish his fruit supply. If it is divisible by 5, then he needs to go hunting. If he does all three tasks at the same time, it means the number of days that have passed is divisible by 2, 3, and 5. This will first happen after the LCM $(2; 3; 5) = 2 \cdot 3 \cdot 5 = 30$ days. Since September has 30 days, the next heavy day will be October 13.

## Grading Criteria.

- Correctly stated that the number of days passed should be divisible by $2, 3, 5$, and correctly concluded that this will happen again after 30 days, the answer is correct - 7 points.
- Correctly determined that this will happen after 30 days, but the answer is incorrect because the student calculated that September has 31 days (this is clearly written in the work), 6 points.
- Correctly determined that this will happen after 30 days, but there is an error $\pm 1$ in finding the date (not due to the previous point) - 4 points.
- Immediately (without justification) stated that this will happen after 30 days, and the date is correctly indicated - 3 points.
- Only the answer "October 13" without justification - 2 points.
- Incorrect example - 0 points.