1994 AMC 12 第 21 题

Question

求下列陈述的反例个数：

“若

N

是各位数字之和为

4

、且没有一位数字为

0

的正奇数，则

N

是质数。”

Find the number of counterexamples to the statement:

“If

N

is an odd positive integer the sum of whose digits is

4

and none of whose digits is

0,

then

N

is prime.”

0

1

2

3

4

满足数字条件的数至多有四位

A number satisfying the digit conditions has at most four digits

把

4

分拆为若干个正整数，列出其中的奇数

List the odd possibilities by composing

4

into positive digits

可能的奇数是

13,31,121,211

和

1111

。数

13,31

和

211

是质数，而

121=11^2

，且

1111=11\cdot101

。所以有

2

个反例。因此正确答案是 C。

The odd possibilities are

13,31,121,211,

and

1111.

The numbers

13,31,

and

211

are prime, while

121=11^2

and

1111=11\cdot101.

Thus there are

2

counterexamples. Thus the correct answer is C.

其他年份的第 21 题