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 June 6th, 2012, 05:26 AM #1 Member   Joined: May 2012 Posts: 86 Thanks: 0 Counting Problem A number is said to be strictly ascendent when every one of its digits is greater than the one before it (For example: 2348, 123, 349, 258 159,etc.). How many strictly ascendent numbers are there between 1-10000? Help is appreciated. June 6th, 2012, 05:55 AM #2 Senior Member   Joined: Apr 2010 Posts: 215 Thanks: 0 Re: Counting Problem Write out all digits in increasing order: We need 4 digits, so scratch 5 of them ( choices!), for example: Now we have 2 choices per digit, whether to scratch it or not. But we can't scratch all of them so we have choices in total for each 4-digit number. So, the final answer is Edit: I think I might have counted some twice. June 6th, 2012, 06:36 AM #3 Member   Joined: May 2012 From: Chennai,India Posts: 67 Thanks: 0 Re: Counting Problem this seems to be a combinatorics problem... Valid digits are 1 5+4 5 6 7 8 9 If single digit nos can be counted as valid, then we have 9 numbers. For 12 to 89: If 1st digit is chosen as n, we have 9-n choices (the next high numbers) to fix the second digit. So , it is 8+7+6+5+4+3+2+1 = 8* 9/2 = 36 numbers For 123 to 789: If 1st and 2nd digit are fixed as 12, we have 7 choice to fill the 3rd digit. If 1st and 2nd digit are fixed as 13, we have 6 choice to fill the 3rd so, it is (7+6+5+4+3+2+1)+(6+5+4+3+2+1)+....(2+1)+1 = 84 numbers For 1234 to 6789: iF first 3 digits are fixed as 123, we have 6 choices to fill 4th digit If firlst 3 digits are fixed as 134, we have 5 choices So, it is (6+5+4+3+2+1)+(5+4+3+2+1)+---(2+1)+1= 56 numbers.. So we have totally 9+36+84+56 = 185 numbers. Any way to do this the number theory way? June 6th, 2012, 08:17 AM   #4
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Re: Counting Problem

Hello, Jakarta!

Quote:
 A number is said to be strictly ascendent when every one of its digits is greater than the one before it. (For example: 2348, 123, 349, 258 159, etc.) How many strictly ascendent numbers are there between 1-10000 ?

[color=beige]. . [/color] June 6th, 2012, 08:23 AM   #5
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Re: Counting Problem

Quote:
Originally Posted by soroban
Hello, Jakarta!

Quote:
 A number is said to be strictly ascendent when every one of its digits is greater than the one before it. (For example: 2348, 123, 349, 258 159, etc.) How many strictly ascendent numbers are there between 1-10000 ?

[color=beige]. . [/color]

That's nice but you forgot single digits. June 6th, 2012, 09:18 AM #6 Math Team   Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408 Re: Counting Problem I didn't think one-digit numbers would be considered "strictly ascendent". Are the digits of "5" in increasing order? June 7th, 2012, 04:05 AM   #7
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Re: Counting Problem

Quote:
 Originally Posted by soroban Are the digits of "5" in increasing order?
I think they are. A number is not ascendent if there are two digits x1 x2 appearing in that order and with x2<=x1. You cannot find two such digits in 5. Tags counting, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post superconduct Algebra 2 January 7th, 2014 10:01 AM zelmac Algebra 0 February 14th, 2013 05:29 AM scream Applied Math 2 February 21st, 2012 11:50 AM kec11494 Applied Math 1 December 20th, 2010 08:44 PM julian21 Applied Math 0 April 27th, 2010 09:48 AM

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