Problem 11 · 2016 Math Kangaroo
Medium
Logic & Word Problems
casework
Peter wants to guess Paul's password. He already knows the following: the three last characters are digits, and there are at most three capital letters in the password. Which of the following passwords could be Paul's?
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Answer: C — 1234LLuuaapp4321
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Hint 1 of 2
Check two rules for each option: the last three characters are digits, and there are at most three capital letters.
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Hint 2 of 2
Eliminate any password that breaks either rule.
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Approach: test each option against both rules
- PAUL123 has four capitals (P, A, U, L) — too many.
- P0a1u2L3 and 123PAUL do not end in three digits, and Paulin3 also fails the last-three-digits rule.
- 1234LLuuaapp4321 ends in 321 (three digits) and has only two capitals (L, L), so it satisfies both rules.
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