Problem 2 · 2008 AMC 8
Easy
Logic & Word Problems
letter-position-decode
The ten-letter code "BEST OF LUCK" represents the ten digits 0–9, in order. What 4-digit number is represented by the code word "CLUE"?
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Answer: A — 8671.
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Hint 1 of 2
The code is a one-to-one key: the 1st letter stands for 0, not 1 — counting starts at zero.
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Hint 2 of 2
Build the lookup table once, then read off the answer; this is just decoding with a substitution cipher.
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Approach: map letter position to digit
- Number the letters from 0: B=0, E=1, S=2, T=3, O=4, F=5, L=6, U=7, C=8, K=9. The trap is starting at 1 — the ten letters cover 0–9, so the first letter is 0.
- Read C-L-U-E off the table: 8-6-7-1 = 8671.
- Shortcut: the choices already start 8… or 9…, so finding just C=8 eliminates two answers instantly.
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