Problem 1 Max has ten cards with the digits 0, 1, 2,…9. He can arrange these cards into different 10-digit numbers. What is the greatest number that he can get?
Answer The greatest number should start with the greatest digit 9. The second digit will be the greatest of the rest, i.e. 8, and so on. The greatest number is 9876543210.
Problem 2 A teacher has four cards with numbers. The sum of these numbers is equal to 8. When the teacher shows these cards to Mary and asks to multiply the numbers, Mary also gets 8. What numbers are on the cards? Some numbers could be equal.