Problem 3 · 2022 Math Kangaroo
Easy
Number Theory
place-value
Beate arranges five cards — 4, 8, 31, 59 and 107 — side by side to make the smallest possible nine-digit number. Which card ends up furthest to the right?
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Answer: B — 8
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Hint 1 of 2
To make the joined number smallest, the cards with the smallest leading digit should sit furthest to the left.
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Hint 2 of 2
Order the five cards by the digit they start with, and see which card ends up last on the right.
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Approach: order the cards by their leading digit
- The five cards start with the digits 1 (107), 3 (31), 4 (4), 5 (59) and 8 (8).
- For the smallest number these leading digits must read in increasing order from left to right, so the cards go 107, 31, 4, 59, 8, giving 107314598.
- The card furthest to the right is 8, so the answer is B.
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