October 16th, 2018, 03:45 AM  #1 
Member Joined: Oct 2012 Posts: 70 Thanks: 0  How many number
How many numbers divisible by 4 can be made from these numbers 1,2,3,4,5,6,7 ?

October 16th, 2018, 04:08 AM  #2 
Senior Member Joined: Dec 2015 From: Earth Posts: 318 Thanks: 42 
While creating the numbers let the last digit be an even number

October 16th, 2018, 04:10 AM  #3 
Senior Member Joined: Oct 2009 Posts: 686 Thanks: 223  
October 16th, 2018, 04:27 AM  #4 
Senior Member Joined: Dec 2015 From: Earth Posts: 318 Thanks: 42 
Find the minimal and maximal number from all created numbers , then set the interval from minimal to maximal Example. $\displaystyle n\in [1,7654321]$ , now find integer part of maximal number $\displaystyle N=int[ \frac{7654321}{4} ]$ 
October 16th, 2018, 04:55 AM  #5 
Newbie Joined: Jul 2018 From: Georgia Posts: 26 Thanks: 5 
Not sure what the rules are, but assuming that you can use each number once and only once, then I see one 1 digit (4) and ten 2 digit possibilities (I could have missed something). Beyond that, here's a hint: The largest number you can create would be: 7,654,312. So for a 7 digit number, and keeping 12 as the last two digits, there are (5 x 4 x 3 x 2) or 120 ways you could arrange the first 5 digits. Since you can do the same thing with any of the other 2 digit numbers at the end, that gives you a total of 120 x 10 or 1,200 possibilities for a 7 digit number. Do the same thing for 6 digit, 5 digit, etc. numbers and you can add them all up. Note that you can't do anything else with 4 as the last number by itself because you don't have a zero. 
October 16th, 2018, 06:32 AM  #6 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,788 Thanks: 970  
October 16th, 2018, 06:59 AM  #7 
Newbie Joined: Jul 2018 From: Georgia Posts: 26 Thanks: 5 
Oh, and this didn't dawn on me until I posted, but it's interesting that there are exactly the same number of possibilities for 6 digit as for a 7 digit number. Seems obvious in retrospect, but I didn't think it through. 
October 16th, 2018, 08:47 AM  #8  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,788 Thanks: 970  Quote:
1st = 123456, last = 765432 If digits 1 to 6, then 192 possibilities...  
October 16th, 2018, 06:09 PM  #9 
Newbie Joined: Jul 2018 From: Georgia Posts: 26 Thanks: 5 
Had a late thought about this. In the original question, change 'divisible by 4' to 'divisible by 6.' Now THAT's an interesting problem. Can't even think about how to approach that at the moment. 
October 16th, 2018, 08:16 PM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,788 Thanks: 970 
Answer will be: none!!


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