Question

The odometer on Mario’s parents’ car reads 28,882 when his father fills it up. Since Mario’s family is going on vacation, his father set the trip odometer to 0 so he will know how many miles long the trip is. To keep Mario and his sister busy during the trip, he gives them the following problems.

a) Mario noticed that there are only 2 different digits in the number 28,882. How far will the car need to travel before all the digits are different? What is that number?
A) 28,883 miles
B) 28,888 miles
C) 28,891 miles
D) 28,892 miles

Answer 1

Mario's car will need to travel 9 more miles from the initial odometer reading of 28,882 to reach a point where all digits are different, which occurs at the odometer reading of 28,891 miles.

Step-by-step explanation:

The odometer on Mario’s parents’ car reads 28,882 when his father fills it up. Mario noticed that there are only 2 different digits in the number 28,882. To find out how far the car will need to travel before all the digits are different, we need to look for the next number where no digits repeat. Starting from 28,882, the next number will be 28,883, but this still has repeating digits. If we increment each digit, we eventually arrive at 28,889, which still has repeating digits; the '8' repeats. One more mile will change the number to 28,890, but this also has repeating zeros. Therefore, we must go to the next number which is 28,891. This is the number where all the digits are different for the first time since the odometer reading was 28,882. So, the correct answer is C) 28,891 miles.