Problem of the Week 19

Suppose the hundreds digit of a three-digit number is greater than the tens digit and the ones digit.  When the digits in the number are reversed and the resulting number is subtracted from the original number, the units digit in the difference is 4.  What is the difference between the three-digit number and its reverse?  How many different three-digit numbers meet the given conditions?

 

Alternate Problem 19

Consider any two-digit number whose digits are not zero and are not the same.  What is the greatest integer that divides evenly the difference between the square of the number and the square of its reverse?

 

Extension Problem 19

Find a four-digit number so that if a decimal point is placed between the hundreds digit and the tens digit, the resulting number is the average of the two-digit whole numbers on either side of the decimal point.