Brain Teasers Worksheet #1 with engaging logic puzzles and riddles for educational use.

Problem 1: Race Order

Question: Five girls participated in a race. Maria finished before Sarah, but behind Ella. Marianne finished before Julia, but behind Sarah. In what order did the girls finish the race?

#### Solution:
We are given the following clues:
1. Maria finished before Sarah, but behind Ella.
2. Marianne finished before Julia, but behind Sarah.

Let's break this down step by step:

- From clue 1:
- Maria is behind Ella → Ella > Maria.
- Maria is before Sarah → Maria > Sarah.
- Combining these: Ella > Maria > Sarah.

- From clue 2:
- Marianne is before Julia → Marianne > Julia.
- Marianne is behind Sarah → Sarah > Marianne.
- Combining these: Sarah > Marianne > Julia.

Now, let’s combine all the information:
- From clue 1: Ella > Maria > Sarah.
- From clue 2: Sarah > Marianne > Julia.

Combining both sets of inequalities:
- Ella > Maria > Sarah > Marianne > Julia.

Thus, the order in which the girls finished the race is:
1. Ella
2. Maria
3. Sarah
4. Marianne
5. Julia

#### Final Answer:
\[
\boxed{Ella, Maria, Sarah, Marianne, Julia}
\]

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Problem 2: Employee Schedule

Question: Margaret’s Marvelous Magical Milks is open from 9:00 A.M. to 9:00 P.M. At least one person must be working at all times. The busiest times are Fridays through Sundays between 2:00 P.M. and 9:00 P.M. Each employee’s shift lasts at most 6 hours. There are ten employees who can work no more than 15 hours per week. Design a schedule that works for everyone.

#### Solution:
To design a feasible schedule, we need to ensure:
1. The store is staffed at all times (9:00 A.M. to 9:00 P.M. daily).
2. Coverage is especially strong during peak hours (2:00 P.M. to 9:00 P.M. on Fridays, Saturdays, and Sundays).
3. No employee works more than 15 hours per week.
4. Shifts last at most 6 hours.

#### Step-by-Step Approach:
1. Determine Total Hours Needed Per Day:
- The store is open for 12 hours each day (9:00 A.M. to 9:00 P.M.).
- At least one employee must be present at all times, so we need coverage for 12 hours daily.

2. Shift Structure:
- Each shift is at most 6 hours long.
- To cover 12 hours, we can use overlapping shifts:
- Morning shift: 9:00 A.M. to 3:00 P.M.
- Afternoon shift: 1:00 P.M. to 7:00 P.M.
- Evening shift: 5:00 P.M. to 11:00 P.M.

3. Peak Hours Coverage:
- During peak hours (2:00 P.M. to 9:00 P.M.), additional staff may be needed. We can assign extra employees to overlap shifts during this period.

4. Weekly Workload:
- Each employee can work up to 15 hours per week.
- With 10 employees, we can distribute the workload evenly.

#### Example Schedule:
Here’s a sample weekly schedule for one week (Monday to Sunday):

- Monday to Thursday:
- Morning Shift (9:00 A.M. to 3:00 P.M.): Employees 1, 2, 3, 4 rotate.
- Afternoon Shift (1:00 P.M. to 7:00 P.M.): Employees 5, 6, 7, 8 rotate.
- Evening Shift (5:00 P.M. to 11:00 P.M.): Employees 9, 10 rotate.

- Friday to Sunday (Peak Hours):
- Morning Shift (9:00 A.M. to 3:00 P.M.): Employees 1, 2, 3, 4 rotate.
- Afternoon Shift (1:00 P.M. to 7:00 P.M.): Employees 5, 6, 7, 8 rotate.
- Evening Shift (5:00 P.M. to 11:00 P.M.): Employees 9, 10 rotate.
- Additional Peak Coverage (2:00 P.M. to 9:00 P.M.): Rotate all employees to ensure extra coverage during peak hours.

#### Ensuring Fair Distribution:
- Each employee works approximately 3 shifts per week (totaling 15 hours).
- Rotate employees to ensure fairness and avoid burnout.

#### Final Answer:
A detailed schedule can be created based on the above structure, ensuring that:
- All hours are covered.
- Peak hours have additional staffing.
- No employee exceeds 15 hours per week.
- Shifts do not exceed 6 hours.

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Problem 3: Riddle

Question: Moshe walks across a bridge. He sees a boat full of people, yet there isn’t a single person on board. How is this possible?

#### Solution:
The key to solving this riddle lies in interpreting the phrase "a boat full of people." The word "people" can refer to individuals who are not necessarily human.

In this case, the boat is full of fish. Fish are living beings but are not considered "people" in the human sense. Therefore, the boat can be "full of people" (in a metaphorical or non-human sense) without having any humans on board.

#### Final Answer:
\[
\boxed{\text{The boat was full of fish.}}
\]

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Summary of Solutions:

1. Race Order: \(\boxed{Ella, Maria, Sarah, Marianne, Julia}\)
2. Employee Schedule: A rotating schedule with morning, afternoon, and evening shifts, ensuring coverage during peak hours and limiting each employee to 15 hours per week.
3. Riddle: \(\boxed{\text{The boat was full of fish.}}\)