SUMMARY
The smallest number that is composed of each digit from 1 to 9 exactly once and is divisible by 99 is 123456789. This conclusion is reached by verifying that the number meets the divisibility rules for both 9 and 11, which are required for divisibility by 99. The sum of the digits equals 45, which is divisible by 9, and the alternating sum of the digits equals 0, which is divisible by 11. Therefore, 123456789 is confirmed as the solution.
PREREQUISITES
- Understanding of divisibility rules, specifically for 9 and 11.
- Familiarity with permutations of digits.
- Basic knowledge of number theory.
- Ability to perform arithmetic operations with large numbers.
NEXT STEPS
- Explore advanced number theory concepts related to divisibility.
- Learn about permutations and combinations in mathematics.
- Investigate other divisibility rules for different numbers.
- Study the properties of unique digit arrangements in mathematics.
USEFUL FOR
Mathematicians, educators, students studying number theory, and puzzle enthusiasts interested in combinatorial problems and divisibility challenges.