A positive integer is called a rising number If its digits form a strictly increasing sequence. for example, 1457 is a rising number, 3438 is not a rising number, and neither 2334.
Questions: How many 3-digit rising numbers are there where 3 is the middle digit? (solved) How many three-digit rising numbers are there?
x3y : x can have 2 values, y can be six, so there are 12 rising numbers.
How many three-digit numbers, 9*10*10= ?
the 1st part of the question is a BIG hint for the 2nd part
sum the 1st part solutions for the digits 2 through 8
To find out how many three-digit rising numbers there are, we need to determine the range of possible values for each digit.
Since a three-digit number has three digits, we can break it down into three separate positions: hundreds, tens, and ones.
For a three-digit rising number, the hundreds digit has to be strictly less than the tens digit, and the tens digit has to be strictly less than the ones digit.
To find the number of three-digit rising numbers, we can count the possible values for each digit position.
For the hundreds digit, it can be any number from 1 to 8 because it needs to be strictly less than the tens digit, which can be any number from 2 to 9. The ones digit can be any number from 3 to 9 because it needs to be strictly greater than the tens digit.
Therefore, the number of three-digit rising numbers can be calculated as follows:
Number of possibilities for the hundreds digit: 8 (since it can range from 1 to 8)
Number of possibilities for the tens digit: 7 (since it can range from 2 to 8, excluding the hundreds digit)
Number of possibilities for the ones digit: 7 (since it can range from 3 to 9)
The total number of three-digit rising numbers is obtained by multiplying these possibilities together:
8 * 7 * 7 = 392
So, there are 392 three-digit rising numbers in total.