Grades 11-12 Video Solutions 2022-2022_11-12

Video Transcription

When he looks at the water meter in his bathroom, Tony notices that all the digits on the meter are different, as shown in the diagram.  How much water will be used until the next time all the digits on the meter are different?  So, let's take a look at these digits and see which is the biggest digit we have to increase before we're able to make all the digits different.  So, if we increase this 6 to a 7, 8, or 9, it overlaps with this 7, 8, or 9. So, we can't just increase this one. Okay, what if we start increasing this one?  Well, we can increase it to an 8 or a 9, and that still overlaps. This 8, if we increase it, it overlaps with this 9.  That means we have to increase this 1 to a 2 in order to get anywhere. Okay, well now we have 9, 2, something, something, something.  So, let's just choose the smallest number that does this. We've already used up 2, so we can do 0, 1, 3.  So, if we have 92.013, the amount of water that we used is just this guy minus this guy, which is 0.137.

Video Summary

Tony examines his water meter and finds all digits are unique. To determine the water used until the next time all digits differ, he identifies that increasing the smallest digits causes overlap. By incrementing strategically, he sets the digits to 92.013, which keeps them unique. He calculates the water used by subtracting his current reading from this new value, concluding that 0.137 units of water will be used until all digits are different again.