Integers greater than 1000 are created using the digits exactly once in each integer. What is the difference between the largest and the smallest integers that can be created in this way?
CEMC Cayley
Solution
With a given set of four digits, the largest possible integer that can be formed puts the largest digit in the thousands place, the second largest digit in the hundreds place, the third largest digit in the tens place, and the smallest digit in the units place. Thus, the largest integer that can be formed with the digits is 3210. The smallest integer of this type that can be made uses a thousands digit of 1, and then lists the remaining digits in increasing order; this integer is 1023. The difference between these integers is .
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