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Array Size Coupled to Content

What is P(len==4) under tuple counting, and why does this puzzle still demonstrate bidirectional solving?

Puzzle

Difficulty: Hard · Puzzle 6 of 6 · Topic: Constraint Solving Order Puzzles

What is P(len==4) under tuple counting, and why does this puzzle still demonstrate bidirectional solving?

Code

systemverilog

class size_content;
  rand int unsigned len;
  rand byte data[];
  constraint c {
    len inside {[2:4]};
    data.size() == len;
    foreach (data[i]) data[i] == i;
  }
endclass

Hint

For each legal len, how many distinct data arrays satisfy foreach equality?

Step-by-step solution

diagram

1) len can be 2,3,4.
2) For each len, foreach constraint fixes data uniquely to {0..len-1}.
3) So each len contributes exactly one legal tuple in joint space.
4) Total tuples=3 and exactly one has len==4 -> P(len==4)=1/3.

Answer

Answer: P(len==4)=1/3; size and content are solved together, and content constraints can reduce tuple multiplicity to one per size.

Why candidates get it wrong

People assume longer arrays automatically imply more solutions, but deterministic element constraints can cancel that effect.

Interviewer follow-up

How would allowing data[i] inside {[0:1]} change len bias?

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