Problem 22 · 2017 Math Kangaroo
Stretch
Logic & Word Problems
casework
Each of the 5 keys opens exactly one padlock. On a padlock, each letter stands for one digit, and equal letters mean equal digits. Which digits are on the key marked with the question mark?
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Answer: C — 284
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Hint 1 of 2
Each padlock's letter pattern (which letters repeat and where) must match a key's digit pattern.
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Hint 2 of 2
Match the all-different padlock to the all-different key, then read off shared letters to decode the rest.
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Approach: match letter patterns to digit patterns and solve for each letter
- The unknown key 284 (all different digits) fits BHD (all different letters): B=2, H=8, D=4.
- DAD = 4_4 matches 414, giving A=1; then ABD = 1,2,4 matches 124 and AHD = 1,8,4 matches 184.
- HAB = 8,1,2 matches 812, so every padlock is accounted for consistently.
- The question-mark key reads 284 (C).
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