Given the following partial frequency map from words: {0b10101: 2, 0b10010: 1} and puzzle "abcde" (letters a,b,c,d,e), which word mask corresponds to a valid word counted for this puzzle if the puzzle's first letter is 'a' (bit 0)?

hard🔄 Reverse Engineer Q9 of Q15

Subsets & Combinations - Number of Valid Words for Each Puzzle

A0b10010 (letters b and d)

B0b10101 (letters a, c, e)

C0b11111 (letters a, b, c, d, e)

D0b01010 (letters b and d)

Step-by-Step Solution

Solution:

Step 1: Check first letter bit
First letter 'a' corresponds to bit 0, so valid word mask must have bit 0 set.
Step 2: Check masks
0b10101 has bit 0 set (positions 0,2,4), 0b10010 does not (bits 1 and 4), so only 0b10101 is valid.
Final Answer:
Option B -> Option B
Quick Check:
Mask 0b10101 includes first letter bit 0 and subset of puzzle letters [OK]

Quick Trick: Valid word mask must include puzzle's first letter bit [OK]

Common Mistakes:

MISTAKES

Ignoring first letter bit requirement
Confusing bit positions

Trap Explanation:

PITFALL

Candidates often pick masks missing first letter bit, causing invalid counts.

Interviewer Note:

CONTEXT

Tests reverse reasoning from frequency map and puzzle constraints

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More Subsets & Combinations Quizzes

Given the following partial frequency map from words: {0b10101: 2, 0b10010: 1} and puzzle "abcde" (letters a,b,c,d,e), which word mask corresponds to a valid word counted for this puzzle if the puzzle's first letter is 'a' (bit 0)?

Step 1: Check first letter bit

Step 2: Check masks

Final Answer:

Quick Check:

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