Problem 15 · 2010 Math Kangaroo
Medium
Arithmetic & Operations
patterndoubling
Hans started a chain e-mail. He sent an e-mail to his friend Peter, who sent it on to 2 more people. Each person who gets the e-mail sends it on to 2 more people. After 3 rounds, 1 + 2 + 4 = 7 people have received the e-mail. How many people have received the e-mail after 5 rounds?
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Answer: C — 31
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Hint 1 of 2
Each round doubles the number of new people: 1, 2, 4, then 8, 16.
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Hint 2 of 2
Add up the new people from all five rounds.
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Approach: sum the doubling rounds
- Each round the number of new people doubles: 1, 2, 4, then 8, then 16.
- Add up all five rounds: 1 + 2 + 4 + 8 + 16 = 31.
- So 31 people have the e-mail, choice C.
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