Work-schedule logic — deducing Nurse Kemp’s consecutive night shifts Nurse Rogers has worked 5 night shifts in a row. Nurse Kemp has worked more consecutive night shifts than Rogers. Nurse Calvin has worked 8 in a row, which is fewer than Kemp. Nurse Miller has worked 15 in a row, more than Kemp and Rogers combined. How many consecutive night shifts has Nurse Kemp worked?

Introduction / Context:
This puzzle involves inequality chaining and a sum constraint. You are given runs of consecutive night shifts for four nurses. The goal is to compute Nurse Kemp’s count using “greater than”, “less than”, and “more than combined” conditions. It is a typical test of bounded reasoning and integer feasibility.

Given Data / Assumptions:

• Nurse Rogers: 5 consecutive night shifts.
• Nurse Kemp: more than Rogers → Kemp > 5.
• Nurse Calvin: 8 consecutive night shifts and less than Kemp → Kemp > 8.
• Nurse Miller: 15 consecutive night shifts, which is more than the sum of Kemp and Rogers → 15 > Kemp + 5.
• All counts are whole numbers.

Concept / Approach:
Convert each statement to numeric inequalities and intersect their solution sets. Because these are small integers, quick arithmetic will reveal the only value that satisfies every condition simultaneously.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• eight: contradicts “Kemp > 8”.
• ten: violates 15 > Kemp + 5 because 10 + 5 = 15 is not “more than”.
• eleven: fails 15 > Kemp + 5 since 11 + 5 = 16.
• seven: violates Kemp > 8 and Kemp > 5.

Common Pitfalls:
Overlooking that “more than combined” uses strict greater than, not greater than or equal to. Also, some solvers forget that all quantities are integers, which is essential for narrowing the value to a single number.

Final Answer:
nine