
Math Events Math Events, Competitions, Meetups  Local, Regional, State, National, International 
 LinkBack  Thread Tools  Display Modes 
April 5th, 2007, 07:18 AM  #1 
Member Joined: Nov 2006 Posts: 54 Thanks: 0  A Decimal Digit Puzzle
Determine the total number of nonnegative integers with not more than 1993 decimal digits having nondecreasing digits. For example, 33455 is a valid instance of such nonnegative integers, while 76 is NOT a valid nonnegative integer having nondecreasing digits. 
April 5th, 2007, 12:40 PM  #2 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0 
Answer > 1993 
April 5th, 2007, 06:24 PM  #3 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
Hey, balls and urns argument! We have 1993 identical objects and nine dividers. The objects before the first divider are 0's, those between the first and second are 1's, etc. We now have 1993+9=2002 total objects, which fall into two categories, the objects in one category being indistinguishable from each other. Therefore, there are 2002!\(1993!9!)≈1.39827649874513*10^24 such numbers. The last three digits of the number should be zeros, so that means we are only three digits shy of having an exact answer (my calculator only uses 15 significant digits). But CRGreathouse should have no problem giving the exact answer! 
April 6th, 2007, 03:28 PM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
 
April 6th, 2007, 06:43 PM  #5 
Senior Member Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 
Hmm, I thought I checked to make sure it had enough 2's, but apparently not. Fortunately, no one caught my missubtraction (2415=9=/=6 [I must have been up too late]).


Tags 
decimal, digit, puzzle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
decimal  blackers1778  Elementary Math  2  March 23rd, 2014 11:42 PM 
need help for decimal  gamemaker825  Algebra  9  April 8th, 2012 10:47 PM 
Decimal To Fraction To Decimal  demipaul  Linear Algebra  2  November 19th, 2009 05:42 AM 
least significant decimal digit  pablo26  Number Theory  4  January 8th, 2009 04:24 PM 
Puzzle : digit sum and powers  momo  Number Theory  10  September 16th, 2008 10:00 AM 