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October 16th, 2018, 03:45 AM   #1
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How many number

How many numbers divisible by 4 can be made from these numbers 1,2,3,4,5,6,7 ?
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October 16th, 2018, 04:08 AM   #2
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While creating the numbers let the last digit be an even number
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October 16th, 2018, 04:10 AM   #3
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Quote:
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While creating the numbers let the last digit be an even number
14
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October 16th, 2018, 04:27 AM   #4
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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
$\displaystyle N=int[ \frac{7654321}{4} ]$
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October 16th, 2018, 04:55 AM   #5
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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.
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October 16th, 2018, 06:32 AM   #6
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1,200 possibilities for a 7 digit number.
Agree.
1: 1234576
2: 1234756
3: 1235476
4: 1235764
...
1197: 7653124
1198: 7653412
1199: 7654132
1200: 7654312
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October 16th, 2018, 06:59 AM   #7
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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.
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October 16th, 2018, 08:47 AM   #8
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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.
....but still using the original 7 digits...not digits 1 to 6...
1st = 123456, last = 765432

If digits 1 to 6, then 192 possibilities...
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October 16th, 2018, 06:09 PM   #9
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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.
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October 16th, 2018, 08:16 PM   #10
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Answer will be: none!!
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