Problem 11 · 1998 AJHSME
Medium
Logic & Word Problems
careful-counting
Harry has 3 sisters and 5 brothers. His sister Harriet has S sisters and B brothers. What is the product of S and B?
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Answer: C — 12.
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Hint 1 of 2
The trap is counting from Harry's view and copying his numbers. Step back and count the whole family — total girls and total boys — then look at it fresh through Harriet's eyes.
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Hint 2 of 2
Nobody counts themselves as their own sibling. Harry is a boy (so he's one of the brothers from a sister's view); Harriet is a girl (so she's one of the sisters from a brother's view).
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Approach: tally the whole family, then re-count from Harriet
- Build the family roster from Harry's view. Harry is a boy with 3 sisters and 5 brothers — but Harry himself is also a boy, so the family has 3 girls and 5 + 1 = 6 boys.
- Now stand in Harriet's shoes. She's one of the 3 girls, so her sisters are the other 2 (she doesn't count herself): S = 2. All 6 boys are her brothers: B = 6.
- So S × B = 2 × 6 = 12.
- Why this transfers: in any sibling puzzle, count the family TOTAL once, then subtract the person you're asking about from their own same-gender group. The 'don't count yourself' slip is the whole point of these problems.
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