How many possible hexadecimal strings of length 4 are there?

Question

BlackTom AI · Accepted Answer

Question restatement: How many possible hexadecimal strings of length 4 are there? Options: 216, 64, 28, 416.

Option 1: 216
- The dataset marks this as the claimed correct answer. In standard counting for hexadecimal strings of length 4, each position can be any of 16 symbols (0–9 and A–F). Therefore, the straightforward count is 16^4 = 65,536, which is not equal to 216. To reach 216 under any conventional interpretation, you would need an altered rule (for example, fixing some positions, restricting the alphabet to a smaller subset, or applying an additional constraint such as a fixed total or a pattern), none of which are stated in the question. Thus, under the normal reading, 216 does not arise from the usual 16-symbol hex alphabet with 4 positions. The correctness of this option relies on an interpretation different from the standard one, which is not specified here.

Option 2: 64
- If we consider a scenario where only a subset of symbols is allowed, 64 could come from 4 choices per position across 4 positions (4^4 = 256, not 64) or from 8 choices across 2 positions (8^2 = 64), but neither aligns cleanly with a length-4 hex string with 16-symbol alphabet. In short, 64 would require a specific restrictive rule that is not described in the prompt, so this option is inconsistent with the usual hex-4-string counting.

Option 3: 28
- A count of 28 would suggest a highly unusual constraint (for example, counting strings that satisfy a particular modular or pattern constraint) or a misapplication of a combinatorial formula. It does not align with the standard 16-symbol hex alphabet and four positions, where the total would be much larger. Without an explicit constraint, 28 cannot be justified for length-4 hex strings.

Option 4: 416
- The number 416 can be seen as 16 × 26, which might tempt a justification like: 16 choices for the first character and 26 for the rest or some split like that. However, hex digits do not include 26 distinct symbols, so multiplying 16 by 26 does not correspond to a valid counting of length-4 hex strings under any conventional interpretation. This option conflates the hex alphabet with the size of the English alphabet, which is a mistaken premise for this problem.

Summary view: The standard counting for hexadecimal strings of length 4 yields 16^4 = 65,536, which is not among the provided options. The presence of 216 as the indicated answer implies either a misprint, a misinterpretation, or an unstated constraint not present in the question. The other options likewise do not correspond to the normal counting of 4-character strings over a 16-symbol alphabet, given no additional restrictions.

Note: If you encounter this in a test, it’s worth verifying the exact wording or any accompanying notes, because the expected count under the standard interpretation should be 65,536, not any of the listed options. The provided answer 216 cannot be justified by the usual definition of hexadecimal strings of length 4 without additional, unstated rules.

DATA STRUCTURES (CS_261_001_S2025) Quiz 1

How many possible hexadecimal strings of length 4 are there?

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