There are six red, yellow and blue beads. How many beads must be pulled out to ensure that the four beads have the same color?

10 beads can ensure that four beads are the same color.

Analysis:

There are six red, yellow and blue beads, so there is a *** 18 bead. To ensure that there are four beads of the same color, it is necessary to calculate according to the lowest probability.

For example, three results may be red, yellow, yellow, blue, red, yellow, yellow, red, blue, yellow, blue, red, yellow and blue, among which the combination of red, yellow and blue requires the most number and the lowest probability.

Therefore, in order to ensure that four beads with the same color can be obtained, it can be expressed as the first red, yellow and blue, the second red, yellow and blue, the third red, yellow and blue, and the fourth one randomly touches a bead, totaling *** 10.

Extended data

Touching beads belongs to the worst principle of pigeon hole principle, that is, considering all possible situations and the most unfavorable situation for something.

For example, 300 people went to the job fair to apply for jobs, including software design 100, marketing 80, financial management 70 and human resources management 50. So how many people can find jobs and at least 70 people can find the same job major?

At this time, the worst case we consider is that 69 people in software design, marketing and financial management will sign up, and all 50 people in human resources management will sign up. Then by enrolling 1 person at this time, it can be determined that 70 people will find the same job major. So at least 69*3+50+ 1=258 people are needed.