6 Digit Number Puzzle
6 Digit Number Puzzle
How many 6-digit numbers can be formed by using the digits 1 to 6 without repetition. Such that the number is divisible by the digit at its unit place?
Solution: 6 Digit Number
Divisibility Rule Analysis
Divisibility Rule of 1
Divisibility Rule of 2
Divisibility Rule of 3
Divisibility Rule of 4
Divisibility Rule of 5
Divisibility Rule of 6
Detailed Analysis
Explanation-
XXXXX1 is always divisible by 1, so we have 5! numbers.
XXXXX2 is always divisible by 2, so we have 5! numbers.
XXXXX3 is always divisible by 3 (sum of digits is always 21), so we have 5! numbers.
XXXXY4 is divisible by 4 only if Y is 2 or 6, so we have 2 \times 4! numbers.
XXXXX5 is always divisible by 5, so we have 5! numbers.
XXXXX6 is always divisible by 6 (even number divisible by 3), so we have 5! numbers.
So total number of numbers with required property
= 5 \times 5! + 2\times 4! = 600 + 48 = 648 numbers.
Prime Course Trailer
Related Banners
Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription
Get over 200+ course One Subscription
Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others
- Flipping Coins Puzzle Answer
- Bag of Forgery Coins Puzzle Answer
- 3 Glass & 10 Coins Puzzle Answer
- Pirates and 100 Coins Puzzle Answer
- Horse Puzzle Answer
- Handshake Puzzle Answer
- Burning Rope Puzzle Answer
- Shopkeeper & the fake note Puzzle Answer
- Heavier Ball Puzzle Answer
- 5L measuring Puzzle Answer
- Gold Bar Puzzle Answer
Login/Signup to comment