Question

There are 120 five-digit numbers that can be made from the digits 1, 2, 3, 4, 5 if each digit is used once in the number. That smallest is 12,345 and the largest is 54,321. If these 120 numbers are listed in order from smallest to largest, what is the 73rd number in the list?

Answer 1

41235

Explanation:

There are 120 five-digit numbers that can be made from the digits 1, 2, 3, 4, 5 if each digit is used once in the number,

The total number of times where each number will occur or be at first place is calculated as:

4! = 4 × 3 × 2 × 1

= 24

Hence,

24th number = The last number where 1 is at first place

We can write this out as:

12345

12354

12435

12453

12534

12543

13245

13254

13425

13452

13524

13542 e.t.c.

48th number = The last number where 2 is at first place

72nd place = The last number where 3 is at first place.

This means, the 73rd number is the first number where 4 is at first place.

Therefore, the 73rd number based on pattern is 41235