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MathNet 2018-part-01 — 181 problems (EN–VI) Question 151

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 151

a) How many four-digit numbers have an even sum of digits?
b) A number with two distinct nonzero digits is called beautiful if its tens digit is greater than its units digit. How many beautiful numbers are there?
c) How many four-digit even numbers can we form using the digits $0,1,2,3,4,5$ without using the same digit twice?
d) What is the average of all 5-digit numbers that can be formed using each of the digits $1,3,5,7$ and $8$ exactly once?