2021 AMC 10 B Fall

Complete problem set with solutions and individual problem pages

Problem 1 Easy

What is the value of 1234+2341+3412+4123 ?(2021 AMC Fall 10B, Question #1)

  • A.

    10,000

  • B.

    10,010

  • C.

    10,110

  • D.

    11,000

  • E.

    11,110

Answer:E

Solution 1:

We see that 1,2,3, and 4 each appear in the ones, tens, hundreds, and thousands digit exactly once. Since 1+2+3+4=10, we find that the sum is equal to 10 \cdot(1+10+100+1000)=(\mathbf{E}) 11,110 Note that it is equally valid to manually add all four numbers together to get the answer.

Solution 2:

We have 1234+2341+3412+4123=1111(1+2+3+4)=(\mathbf{E}) 11,110 .