Problem 4 · 2001 AMC 8
Easy
Number Theory
place-value
The digits 1, 2, 3, 4, and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is
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Answer: E — 9.
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Hint 1 of 2
Leftmost digits matter most for size, so they should be smallest — but one rule overrides that: "even" forces the units digit to be 2 or 4.
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Hint 2 of 2
Satisfy the hard rule (even ending) first, then make everything to its left as small as possible.
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Approach: small digits left, but keep the number even
- The most-significant digits control size most, so we want 1, 2, 3 up front. That parks 4 and 9 in the last two slots.
- But the number must be even, so the units digit is the even one of {4, 9} — that's 4. The 9 is forced into the tens place: 12394.
- So the tens digit is 9. The lesson: when a constraint (here "even") locks one position, honor it first, then greedily minimize the rest left-to-right.
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