In the set of all two-digit natural numbers, if the digits of each number are interchanged, how many numbers have their values diminished consequently?42363345

The two-digit natural numbers range from 10 to 99.

Step 1: Identify the numbers that will be diminished when their digits are interchanged. These are the numbers where the tens digit is greater than the units digit.

Step 2: Count these numbers. They are from 10 to 19 (10 numbers), 20 to 29 (9 numbers), 30 to 39 (8 numbers), 40 to 49 (7 numbers), 50 to 59 (6 numbers), 60 to 69 (5 numbers), 70 to 79 (4 numbers), 80 to 89 (3 numbers), and 90 to 99 (2 numbers).

Step 3: Add up these numbers. 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 = 54.

So, there are 54 two-digit natural numbers that have their values diminished when their digits are interchanged.