2021 Fall AMC 10B Problem 1

What is the value of

1234 + 2341 + 3412 + 4123?

Show solution

Solution

We can add each individual digit, yielding

11,110.

We can also get the sum by noticing that each digit has a sum of

10,

so the sum is equal to

10\cdot 1111 = 11,110.

Thus, the answer is E .

Concepts: place value · pairing and grouping

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