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2021 Fall AMC 12B Problem 1

Problem 1 of 25EasierNumber Theory

What is the value of 1234+2341+3412+4123?1234 + 2341 + 3412 + 4123?

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Solution

Each of the digits 1,2,3,41, 2, 3, 4 appears exactly once in the thousands, hundreds, tens, and units columns. So each column sums to 1+2+3+4=10.1 + 2 + 3 + 4 = 10. The total is therefore 101111=11110.10 \cdot 1111 = 11110. Thus, the correct answer is E.

More practice

Concepts: place value · symmetry

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.