Number identification with compound conditions: A number is greater than 44^2 and smaller than 45^2. It is also a multiple of 5, and one part of the number is the square of 6 (i.e., 36 appears as a contiguous part). Determine the number from the options, if possible.

Introduction / Context:
This is a constrained search problem over a narrow numeric band. The number must lie strictly between two consecutive squares (44^2 and 45^2), be a multiple of 5, and visibly contain “36” as a contiguous part (interpreting “one part of the number is the square of 6”). We evaluate the candidates against all constraints.

Given Data / Assumptions:

• Bounds: 44^2 = 1936 and 45^2 = 2025.
• Number must satisfy: 1936 < N < 2025.
• N is a multiple of 5 → last digit is 0 or 5.
• “One part is the square of 6” → the string “36” appears contiguously in N.

Concept / Approach:
List multiples of 5 in (1936, 2025): 1940, 1945, 1950, …, 2020. Then check whether “36” appears in each candidate. If none satisfy all constraints, the problem cannot be resolved to a specific option from the provided list.

Step-by-Step Solution:
Enumerate candidates from options first: 1940 and 1980 fall within (1936, 2025); 2080 exceeds 2025.Check “36” presence: 1940 → digits “1 9 4 0” (no “36”); 1980 → digits “1 9 8 0” (no “36”).Therefore, no given in-range multiple of 5 includes the substring “36.”Conclusion from provided choices: no unique valid number can be selected.

Verification / Alternative check:
Border values 1936 and 2036 either equal 44^2 (not strictly greater) or exceed 45^2 (not strictly smaller). Hence they are disqualified.

Why Other Options Are Wrong:
1940 and 1980 satisfy the range and multiple-of-5 conditions but fail the “contains 36” condition; 2080 is outside the range; “None of these” would claim an alternative exists, but the stem restricts selection to the options. Hence the safest provided choice is “Cannot be determined.”

Common Pitfalls:
Assuming “part” means any arithmetic component rather than a visible contiguous part; including endpoints 1936 or 2025; overlooking the multiple-of-5 constraint.

Final Answer:
Cannot be determined