AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 25 Hard

Using the digits to form a five-digit number (each digit used at most once), such that the difference between any two adjacent digits is at least . How many such five-digit numbers are there?

Answer:C

Starting with : numbers — ;

so starting with , there are also numbers.

Starting with : numbers — ;

so starting with , there are also numbers.

Starting with : numbers — .

Therefore, the total number of such five-digit numbers is