VLSI DV Interview Puzzles · All levels

m<n Cardinality Bias

Compute P(n==4) without solve-before, then estimate what solve n before m does.

Puzzle

Difficulty: Medium · Puzzle 4 of 6 · Topic: solve...before Bias Puzzles

Compute P(n==4) without solve-before, then estimate what solve n before m does.

Code

systemverilog

class sb_mn;
  rand int unsigned n;
  rand int unsigned m;
  constraint c {
    n inside {[1:4]};
    m inside {[0:3]};
    m < n;
  }
  // Variant: solve n before m;
endclass

Hint

Count legal m values for each n.

Step-by-step solution

diagram

1) n=1 allows m={0} (1 tuple), n=2 allows {0,1} (2), n=3 allows {0,1,2} (3), n=4 allows {0,1,2,3} (4).
2) Total tuples = 1+2+3+4 = 10.
3) Baseline P(n==4)=4/10=0.4.
4) With solve n before m, many solvers choose n near-uniform first (~1/4 each), then solve m in chosen branch.
5) Legal solutions are unchanged.

Answer

Answer: Without solve-before, P(n==4)=40%; with solve n before m, n often moves toward ~25% each value while legal tuples stay the same.

Why candidates get it wrong

A common mistake is saying n is uniform just because its domain is 1..4.

Interviewer follow-up

How would you keep tuple-order solving but still get n uniform?

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