Grades 7-8 Video Solutions 2025-2025_7-8

Video Transcription

Problem number 10. The real combination for the bicycle lock shown in the picture is 0000. However, when someone looks at it from the side, they see 8888. When Paul looks at the  combination of his friend's lock from the side, he sees 2815. What is the real combination of  his friend's lock? To solve this problem, let's imagine what each of the dials of the locks looks  like. We know that each of the values appears on each lock from 0 to 9 in order. For each wheel,  we know that the real value appears two places after the value on the side. For example, in the picture, we can see that the real value of 0 actually appears two places after the 8.  This means that we can find the real value by just adding 2 to each of the numbers on the lock,  but we have to remember to wrap the edges. 8 will actually go to 0, not 10, and 9 will actually go  to 1, but not 11. And in this way, you can take any side combination and convert it into the  real combination by adding 2 to each of the digits because we know each of the dials of the lock work the same way. In this case, the combination 2815, if we add 2 to each of the  digits, 2 becomes a 4, 8 becomes a 0 like shown in the picture, 1 becomes a 3, and 5 becomes a 7.  So the resulting real combination will be 4037, and this is option A. So the answer is A, 4037.

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