Math Problem Statement

make numbers 1 through 50 with numbers 1, 2, 3, and 4 using each one once and use all digits

Solution

To construct numbers from 1 through 50 using only the digits 1, 2, 3, and 4 exactly once in each number, while ensuring that all digits are used, the numbers that can be formed are as follows:

  • 12
  • 13
  • 14
  • 21
  • 23
  • 24
  • 31
  • 32
  • 34
  • 41
  • 42
  • 43

These numbers use the digits 1, 2, 3, and 4 exactly once in each number.

Further Questions

  1. Can you form numbers higher than 50 using only 1, 2, 3, and 4 each exactly once?
  2. How many different numbers can you form if you allow three digits?
  3. What is the highest number you can form with these digits?
  4. What combinations of digits would form prime numbers within this range?
  5. How would the set of numbers change if repetition of digits were allowed?

Tip: When constructing numbers with specific digits, consider systematically checking each combination to ensure all possibilities are covered.