Digit Problems
- Use \(3,4,5,6,7,8\) to make digits between 5,000 & 6,000.
- 2, 3, 4, 5, 6, 7: 6-digit numbers not divisible by 5
- 5, 6, 7, 8, 0: Five digit numbers divisible by 4.
- Make 7-digit numbers using 3, 4, 5, 5, 3, 4, 5, 6, keeping odd digits at odd positions, without using digits more than its frequency.
- Use 1, 2, 3, 4, 5, 6, 7, 8, 9 to make numbers with even digits at beginning and end, using each digit only one.
- Form numbers with 0, 3, 5, 6, 8 greater than 4000, without repeating any digit.
- 4-digits and starts with 5 \(\rightarrow 1 \times \space ^5P_3\)
- □ □ □ □ □ □ \(\rightarrow 5! \times \space ^5P_1\) or 6!-5!
- Last two: 56,68, 76 and 60, 08, 80 \(\rightarrow 3! \times ^3P_1 + ^2P_1 \times 2! \times ^3P_1=18+12=30\)
- Odd positions = 4, even = 3; there are repetitions. \(\rightarrow \frac {4!}{2!2!} \times \frac{3!}{2!}=18\)
- \(^4P_1 \times ^3P_1 \times 7! = 60480\) or \(^4P_2 \times 7!\)
- □ □ □ □ + □ □ □ □ □ \(\rightarrow ^3P_1 \times ^4P_3 + ^4P_1 \times 4! = 168\)
- Make meaningful odd numbers using the digits 6, 5, 2, 3, 0 once in each number.
- Make meaningful even numbers using 5, 3, 2, 6, 0.
- Use 1, 2, 3, 4 to make 3 or less-digit numbers by using digits more than once/any no. of times
- \(^2P_1 \times ^3P_1 \times 3!=36\)
- 2 at end, 6 at end, 0 at end \(\rightarrow 2 (1 \times 4!-3!)+4!\)
- 1-digit + 2-digit+3-digit (□ □ □) \(\rightarrow ^4P_1+4 \times 4 + 4^3\)