A Digit Puzzle
Number Theory
Level
pending
All possible 6-digit numbers are formed using 1, 1, 2, 3, 4, 5 exactly once. All these numbers are arranged in ascending order in a row to form a new large single number.
What will be the 1730th digit from the right of this number?
The answer is 2.
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1 solution
Total number of 6-digit numbers possible = 2 ! 6 ! = 360
Therefore, total digits in the number are: 360 x 6 = 2160
1 7 3 0 t h digit from the right is the same as (2160 - 1729) = 4 3 1 s t digit from the left.
Think through logically:
Numbers starting with 11 = 4! = 24; Number of digits = 24 x 6 = 144
Numbers starting with 12 = 4! = 24; Number of digits = 24 x 6 = 144
Numbers starting with 13 = 4! = 24; Number of digits = 24 x 6 = 144
Adding 144 three times gives us 432. This means we can stop at 13. We need not go further.
In other words, there are 432 digits till the unit digit of the last number 135421. Given, we are looking for 4 3 1 s t digit, the answer is 2 .