Create six 3-digit numbers using only the digits 5 and 8. Then, form 3-digit numbers using the digits 9, 5, and 6 exactly once. Finally, use the digits 1, 3, 7, and 9 to form six 4-digit numbers witho

Here are the solutions to the questions:

Q1: Make six 3-digit numbers using 5 and 8.

To form 3-digit numbers using only the digits 5 and 8, one of the digits must be repeated.

• Step 1: Consider numbers with two 5s and one 8, or two 8s and one 5.

  • Numbers with two 5s and one 8: 558, 585, 855
  • Numbers with two 8s and one 5: 885, 858, 588

• Step 2: List six unique 3-digit numbers.

  • The six 3-digit numbers are: $\boxed{\text{558, 585, 855, 885, 858, 588}}$

Q2: Form 3-digit numbers by using the digits 9, 5, and 6.

To form 3-digit numbers using each of the digits 9, 5, and 6 exactly once, we find all possible permutations.

• Step 1: Arrange the digits in all possible orders.

  • Starting with 9: 956, 965
  • Starting with 5: 596, 569
  • Starting with 6: 695, 659

• Step 2: List all the 3-digit numbers formed.

  • The 3-digit numbers are: $\boxed{\text{956, 965, 596, 569, 695, 659}}$

Q3: Use 1, 3, 7, and 9 to form six 4-digit numbers without repeating any digit.

To form 4-digit numbers using each of the digits 1, 3, 7, and 9 exactly once, we find permutations. We only need to list six of them.

• Step 1: Arrange the digits in different orders to form unique 4-digit numbers.

  • Start with 1: 1379, 1397
  • Start with 3: 3179, 3197
  • Start with 7: 7139, 7193

• Step 2: List six unique 4-digit numbers.

  • Six 4-digit numbers are: $\boxed{\text{1379, 1397, 3179, 3197, 7139, 7193}}$