AMC 8 2003 Problem 14

AMC8 2003 年第 14 题

奇偶性★★★☆☆

In this addition problem, each letter stands for a different digit:

\begin{array}{r} TWO \\ +TWO \\ \hline FOUR \end{array}

If T = 7 and the letter

O

represents an even number, what is the only possible value for

W

在上面的加法竖式中，每个字母代表一个不同的数字。若 T = 7 且字母

O

代表一个偶数，则

W

的唯一可能值是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Since both

T

's are 7, then

O

has to equal 4, because 7 + 7 = 14. Then,

F

has to equal 1. To get

R

, we do 4 + 4 (since O = 4 ) to get R = 8. The value for

W

then has to be a number less than 5, otherwise it will change the value of

O

, and can't be a number that has already been used, like 4 or 1. The only other possibilities are 2 and 3. 2 doesn't work because it makes U = 4, which is what

O

already equals. So, the only possible value of

W

is 3

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