Thanks a lot for your feedback! We are happy that you enjoy our Daily Challenge Course and find it useful.

We try to create our course materials and structure so that we teach others not just how to solve one particular problem, but teach how one should think about it, in order to solve many other problems as well as learn different tricks and strategies that could be useful in the future!

Making mistakes is normal! The question is how to use your mistakes to improve yourself and move forward.

We are looking forward to hearing from you again!

"How many 3-digit numbers can you make with the digits ___...?"

"How many numbers have digits that are consecutive..?"

"How many 2-digit numbers do not contain the digit 0...?"

"What is the probability that a random 3-digit number has a zero as a digit...?"

...then after awhile (maybe after making some mistakes along the way!), you learn to be prepared to watch for the tricky zero digits. A number can't start with 0. It's something good to keep in the back of your head!

]]>I'm assuming that you mean that we should subtract ways like 122 and 223 from the 900 total ways to make a three-digit number.

The question said that we cannot have numbers that have more than two digits that are the same. So, actually, it's okay to have numbers like 122 and 223 that have just two digits that are the same. The numbers that won't work are the ones that have three digits that are the same, like 111, 222, 333, etc.

I hope this helps! Please don't hesitate to ask if you have any more questions!

Happy Learning,

The Daily Challenge Team

]]>[Originally posted in Discussions]

I'm not sure what you're confused about, is it the challenge problem or the mini-question at the end of the video?

It might not look like it, but the problems are very similar! In the challenge problem, we wanted to count up all the 3-digit numbers, except those that are like 111 or 999. Those guys are the bad guys! We don't want to count them.

As Professor Loh showed, there are a total of 900 3-digit numbers, right? Out of those 900, there are 9 "bad" guys. They are: 111, 222, 333, 444, 555, 666, 777, 888, and 999. Since we don't want the bad guys in our count, we have to remove them from the 900 numbers, so that's why the answer was 900 - 9 = 891.

In the question at the end of the video, the "bad guys" are different! This time, we don't want to count numbers whose digits go up by 1 each time, or go down by 1 each time. So, 123, 234, 789 are bad, and 210, 321, 987 are also bad. Can you count up how many bad numbers there are?

For the bad guys that go up, they are 123, 234, 345, 456, 567, 678, and 789. 012 is not a bad guy, because it's actually just a 2 digit number (and we aren't looking at 2 digit numbers in the first place!). You can see that there are 7 of them. A quick way to figure this out is by looking at the first digit: It goes from 1 to 7.

For the bad guys that go down, they are 987, 876, 765, 654, 543, 432, 321, and 210. That last one might have been easy to miss! This time there are 8 of them. You can just count them up, but a cool trick you could use is to see that the first digit goes from 9 to 2, and you can do (9 - 2) + 1 = 8. (Can you figure out why this works?)

That means there are 7 + 8 = 15 bad guys in total. We don't want to count them, so we have to take them away from the 900 3-digit numbers that we want to count. So we do 900 - 15 = 885, and that's the answer.

Hopefully that cleared up your confusion! If it was something else that you're confused about, or if you're still confused, please tell us right away and we'll be sure to help.

Happy learning!

Thomas

The Daily Challenge Team

This was a great video. I really liked how the Professor showed the two methods of solving the problem - the multiplication principle plus the principle of working out the total number of numbers between 991 and 100. He also explained why you added one more (with the analogy of a step really well). Great videos and course!

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