Question

通过插入括号，表达式可以得到若干个值。能得到多少个不同的值？ $2\times3+4\times5$

By inserting parentheses, it is possible to give the expression $2\times3+4\times5$ several values. How many different values can be obtained?

$2$

$3$

$4$

$5$

$6$

四个数和三个运算共有五种完整的加括号方式。逐一计算可得

$((2\times3)+4)\times5=50$ ，而 $(2\times(3+4))\times5=70$ 。

$(2\times3)+(4\times5)=26$ 。

$2\times((3+4)\times5)=70$ ，而 $2\times(3+(4\times5))=46$ 。

因此不同的结果是 $26, 46, 50$ 和 $70$ ，共 $4$ 个。

所以正确答案是 C。

There are five full parenthesizations of four numbers joined by three operations. Evaluating all five gives

$((2\times3)+4)\times5=50$ and $(2\times(3+4))\times5=70.$

$(2\times3)+(4\times5)=26.$

$2\times((3+4)\times5)=70$ and $2\times(3+(4\times5))=46.$

Thus the distinct values are $26, 46, 50,$ and $70,$ for a total of $4.$

Thus, the correct answer is C.