Problem 11 · 2012 Math Kangaroo
Medium
Number Theory
place-valuecareful-counting
From the digits 1, 2, 3, 4, 5, 6, 7, 8 we form two four-digit numbers so that every digit is used exactly once and the sum of the two numbers is as small as possible. What is the value of this sum?
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Answer: C — 3825
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Hint 1 of 2
The two thousands-digits matter most for the size of the sum.
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Hint 2 of 2
Put the smallest available digits in the highest place values of both numbers.
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Approach: smallest digits in the biggest places
- To make the sum small, give the two thousands places the smallest digits (1 and 2), the hundreds places 3 and 4, the tens 5 and 6, the units 7 and 8.
- Sum = 1000(1+2) + 100(3+4) + 10(5+6) + (7+8) = 3000 + 700 + 110 + 15 = 3825.
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