perplexus.info :: Just Math : The Descending Integers

The Descending Integers (Posted on 2006-02-02)

Let us consider all possible positive whole numbers (not containing any leading zeroes) with the proviso that in each of the numbers, none of its digits can be repeated.

Note: any given number may or may not contain all the digits from 0 to 9 (Examples: 7; 20; 1056; 3067941825 etc.)

These numbers are now arranged in descending order of magnitude.

What would be the 200,136th number?

See The Solution Submitted by K Sengupta

Rating: 2.8000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: solution I agree

| Comment 2 of 8 |

(In reply to solution by Charlie)

The first 40,320 (= 8!) 10-digit numbers begin 98...

The next 40,320 (= 8!) 10-digit numbers begin 97...

The next 40,320 (= 8!) 10-digit numbers begin 96...

The next 40,320 (= 8!) 10-digit numbers begin 95...

Giving 161, 280 so far, 38,856 to go.

The next 5,040 (= 7!) 10-digit numbers begin 948...

The next 5,040 (= 7!) 10-digit numbers begin 947...

The next 5,040 (= 7!) 10-digit numbers begin 946...

The next 5,040 (= 7!) 10-digit numbers begin 945...

The next 5,040 (= 7!) 10-digit numbers begin 943...

The next 5,040 (= 7!) 10-digit numbers begin 942...

The next 5,040 (= 7!) 10-digit numbers begin 941...

Another 35,280, giving 196,580 so far, 3,576 to go.

The next 720 (= 6!) 10-digit numbers begin 9408...

The next 720 (= 6!) 10-digit numbers begin 9407...

The next 720 (= 6!) 10-digit numbers begin 9406...

The next 720 (= 6!) 10-digit numbers begin 9405...

Another 2,880, giving 199,440 so far, 696 to go.

The next 120 (= 5!) 10-digit numbers begin 94038...

The next 120 (= 5!) 10-digit numbers begin 94037...

The next 120 (= 5!) 10-digit numbers begin 94036...

The next 120 (= 5!) 10-digit numbers begin 94035...

The next 120 (= 5!) 10-digit numbers begin 94032...

Another 600, 96 to go.

The next 24 (= 4!) 10-digit numbers begin 940318...

The next 24 (= 4!) 10-digit numbers begin 940317...

The next 24 (= 4!) 10-digit numbers begin 940316...

The next 24 (= 4!) 10-digit numbers begin 940315...

The required number is the last of these 9,403,152,678.

Posted by goFish on 2006-02-02 12:38:48

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