Number Guessing, lucky number
Using each of the numbers 1, 2, 3, 4, 5, 6, 7 exactly once each time, we can form 7! = 5040 distinct 7-digit numbers.
If these numbers are listed in increasing order, find the number in the list.
The answer is 3657421.
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If we analyze the said problem, we could conclude that there are only 5040th digit from this 7 digit number. 7654321 is the highest number we could form in 7 digit number. Thus, 7654321 is the 5040th number .
By permutation.....
1_ _ _ _ _ _ =720th
2_ _ _ _ _ _=2(720th)
3_ _ _ _ _ _=3(720th) = 2160th, we passed the 2016th.But if we need to find the the 2160th the number is the highest number starting with digit 3, which is 3765421. we have a 2160th number, 3765421, going backward we need to subtract the permutation of the remaining digits.
36_ _ _ _ _= 2160th-120 = 2040th. Then we could come up with the number 2040th which is 3765421. We cannot use anymore 7 in second digit because we subtract then we didn't reach 2016th but 2040th which is the number 3765421.
36_ _ _ _ _=2040- 5!= 1920th. Again we passed 2016th. Then we cannot used the highest digit number in third place . Because we subtract .
365_ _ _ _ =2040-4! = 2016th. Here we can used the highest digit number . 3657421 is the highest number which is the 2016th number ..