Phase 1: Owning the Dataset
Timeline Visualization
6:00am ----[Sleep Time]----[Prep Time]---- 6:40am
(snoozes × 4 min) (remaining) = 40 min total
Key Constraints:
- Initial rating: 10 points
- Total time available: 40 minutes
- Each snooze: 4 minutes
- Preparation penalty: -5 points if >25 min OR <10 min
- Snooze penalty: -1 point for each press after 3rd
Phase 2: Understanding the Question
We need to find:
- Rating: The maximum work-readiness rating achievable
- Snoozes: The number of snooze button presses to achieve that rating
The relationship is: \(\mathrm{Preparation\ time} = 40 - (\mathrm{snoozes} \times 4)\)
Phase 3: Finding the Answer
Let's systematically check each possible number of snoozes:
0 snoozes: Sleep = 0 min, Prep = 40 min
- Prep > 25 → -5 points
- \(\mathrm{Rating} = 10 - 5 = 5\)
1 snooze: Sleep = 4 min, Prep = 36 min
- Prep > 25 → -5 points
- \(\mathrm{Rating} = 10 - 5 = 5\)
2 snoozes: Sleep = 8 min, Prep = 32 min
- Prep > 25 → -5 points
- \(\mathrm{Rating} = 10 - 5 = 5\)
3 snoozes: Sleep = 12 min, Prep = 28 min
- Prep > 25 → -5 points
- \(\mathrm{Rating} = 10 - 5 = 5\)
4 snoozes: Sleep = 16 min, Prep = 24 min
- Prep = 24 (between 10-25) → no prep penalty ✓
- 4 > 3 → -1 point for extra snooze
- \(\mathrm{Rating} = 10 - 1 = 9\) ← Maximum found!
5 snoozes: Sleep = 20 min, Prep = 20 min
- Prep = 20 (between 10-25) → no prep penalty ✓
- 5 > 3 → -2 points for 2 extra snoozes
- \(\mathrm{Rating} = 10 - 2 = 8\)
6 snoozes: Sleep = 24 min, Prep = 16 min
- Prep = 16 (between 10-25) → no prep penalty ✓
- 6 > 3 → -3 points for 3 extra snoozes
- \(\mathrm{Rating} = 10 - 3 = 7\)
Phase 4: Solution
The maximum rating Javier can achieve is 9, obtained by pressing the snooze button 4 times.
This gives him:
- 16 minutes of extra sleep
- 24 minutes to prepare (within the optimal 10-25 minute range)
- Only 1 penalty point for the 4th snooze press
Final Answer: