Grades 7-8 Video Solutions 2021-video 2021 7-8/4

Video Transcription

Question four. How many four-digit numbers have the property that their digits from left to right are consecutive and in ascending order?  Consecutive numbers means that they are in order. For example, 1, 2, and 3 would be consecutive numbers. 1, 2, and 4 would not be, since we would be skipping the  number 3. And in ascending order means that the numbers increase each time. So 3, 2, and 1 are consecutive, but they are descending as opposed to ascending. So to  find out the total number of four-digit numbers that have this property, we can start off with the digit 1. If we wanted to make it ascend, we would do 2 next.  And since it is a four-digit number, we make the number 1,234. The next smallest four-digit number that has this property will begin with a 2, and it will be 2,345.  We can keep doing this until we get to the number 6,789. Since this number ends with a 9, there is no single-digit number that is larger than 9, so we  cannot keep increasing. This means we have our solution, B, six numbers.

Video Summary

The problem asks for the count of four-digit numbers whose digits are consecutive and in ascending order from left to right. Starting with the digit 1, the corresponding number is 1,234. Continuing this pattern, the numbers progress as 2,345, 3,456, and so on, up until 6,789. Digit arrangements beyond 6,789 aren't possible as there isn't a subsequent digit larger than 9. Consequently, there are six such four-digit numbers: 1,234; 2,345; 3,456; 4,567; 5,678; and 6,789.

Keywords

consecutive digits

ascending order

four-digit numbers

number pattern

digit sequence