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2012 AMC 10B Problem 20

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2012 AMC 10B Problem 20AMC 10 Step by Step

Name: Date: September 13, 2026

Games & Processes · difficulty 3 of 5 · about 5 min · position P16-20

Bernardo and Silvia play the following game. An integer between 0 and 999, inclusive, is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds 50 to it and passes the result to Bernardo. The winner is the last person who produces a number less than 1000. Let $N$ be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of $N$ ?

A)
$7$
B)
$8$
C)
$9$
D)
$10$
E)
$11$

2012 AMC 10B Problem 20

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