Question

求下式的值： $1234 + 2341 + 3412 + 4123\text{。}$

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

$10{,}000$

$10{,}010$

$10{,}110$

$11{,}000$

$11{,}110$

每个数字都在每个数位上出现一次。

Each digit appears once in each place value

每一列的数字和都是 $10$ 。

The digit sum in each column is $10$

逐位相加，得到 $11,110$ 。

也可以注意到每个数位上的数字和均为 $10$ ，所以总和为 $10\cdot 1111 = 11,110$ 。

所以答案是 E。

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 .