Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

Problem 1. A gray circle with two holes is put on top of a clock face as shown. The gray circle is turned around the center so that the number 10 appears in  one hole. Which numbers is it possible to see on the other hole? Okay, for this question we can see immediately that the gray circle leaves exactly two numbers  exposed and notice that in the right picture it's 1 and 5 that are exposed. Therefore, one hole shows a time that's four hours after the other or it can be  a hole that's four hours before the other because those are functionally the same thing. Therefore, if the number 10 appears then four hours after 10 is 2  and four hours before 10 is 6. So 2 and 6 can appear and A is the correct answer.

Video Summary

The problem involves determining which numbers can be seen when a gray circle with two holes is placed over a clock face and rotated so the number 10 appears in one hole. Observing the pattern, when one hole shows a number, the other hole shows the number that is four hours ahead or behind. Therefore, if the number 10 is visible, the potential numbers for the other hole are 2 (four hours after) and 6 (four hours before). Thus, the possible numbers visible are 2 and 6, making option A the correct answer.

Keywords

clock face

rotation

number visibility

gray circle

pattern observation