2007 AMC 10B Problems/Problem 9
Problem
A cryptographic code is designed as follows. The first time a letter appears in a given message it is replaced by the letter that is place to its right in the alphabet (asumming that the letter is one place to the right of the letter ). The second time this same letter appears in the given message, it is replaced by the letter that is places to the right, the third time it is replaced by the letter that is places to the right, and so on. For example, with this code the word "banana" becomes "cbodqg". What letter will replace the last letter in the message
Solution
Since the letter that will replace the last does not depend on any letter except the other 's, you can disregard anything else. There are 's, so the last will be replaced by the letter places to the right of . Every places, you will end up with the same letter so you can just take the remainder of when you divide by which is Therefore, the letter that will replace the last is
See Also
2007 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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