Required Mathematical Intelligence

Chapter 95

There are 40 students lined up facing the teacher, starting from 1 to count in turn, after the counting is completed, the teacher asks the students whose count is a multiple of 4 to turn back, and then asks the students whose count is a multiple of 6 to turn back .At this time, how many people are facing the teacher?

[Answer: For this question, it seems very simple, that is, remove all multiples of 40 from 4 people, remove all multiples of 6, and add the common multiples of 4 and 6.It would be a mistake to think that way.What is worth reminding everyone here is to clarify the meaning of "turn backward".

In fact, among the 40 people, 4 people reported that the number was a multiple of 10, 6 people reported that the number was a multiple of 6, and 4 people reported that the number was both a multiple of 6 and a multiple of 3. After turning back, it is already facing the teacher.

Think of it this way:
For the first time, the teacher asked students whose numbers were multiples of 4 to turn back, and there were 40-10=30 students facing the teacher.

第二次老师请报数为6的倍数的学生向后转，因为40人中是6的倍数的有6人，这6人中有3个既是4的倍数，又是6的倍数，两次后转已面对老师，但另3个（6的倍数学生）向后转，恰是背对老师，虽然这6个人方向都发生了变化，但面向老师的人数却是没有变的。所以原题的答案应是：40-10—3 3=30人。]
(End of this chapter)