13 Oct 07
ok this will be very easy as i got it in just a few seconds myself but its fun to do nonetheless. find a number that is:
a number between 1 & 36
two digits
a multiple of 3
when the digits are added together the sum is between 4 & 8
is odd
when you multiply the digits the product is between 4 & 8
what is the number?
13 Oct 07
Originally posted by tournymangr15 r 17
ok this will be very easy as i got it in just a few seconds myself but its fun to do nonetheless. find a number that is:
a number between 1 & 36
two digits
a multiple of 3
when the digits are added together the sum is between 4 & 8
is odd
when you multiply the digits the product is between 4 & 8
what is the number?
14 Oct 07
Originally posted by joe shmoYup, it's a way to check if a number is a multiple of three;
Has anyone noticed the sum of the digits of multiples of 3 repeat 3,6,9 up until 39 which its sum is 12, which has a sum of 3 restarting the sequense replacing a sum of 12 fo three. can anyone explain this?
Have a number abc (where a, b and c stand for the single digits of a three-digit number).
You can write it as a * 100 + b * 10 + c * 1
a * 99 is a multiple of 3, as well as b * 9.
So abc is a multiple of three
if and only if
a * 1 + b * 1 + c * 1 = a + b + c is a multiple of three.
This works for all numbers.
So to check if 123456723 is a multiple of three, we calculate 1+2+3+4+5+6+7+2+3 = 33.
To check if 33 is a multiple of three, we calculate 3+3 = 6
6 is a multiple of 3, so 123456723 is a multiple of three as well.
You have a similar trick for multiples of 9 (sum of digits must be 9 then) and multiples of 11 (alternating sum of digits must be 0).
There is even one for multiples of 7, but that's a bit trickier.
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14 Oct 07
Originally posted by TheMaster37Thanks, I find that interesting.
Yup, it's a way to check if a number is a multiple of three;
Have a number abc (where a, b and c stand for the single digits of a three-digit number).
You can write it as a * 100 + b * 10 + c * 1
a * 99 is a multiple of 3, as well as b * 9.
So abc is a multiple of three
if and only if
a * 1 + b * 1 + c * 1 = a + b + c is a multiple of ...[text shortened]... sum of digits must be 0).
There is even one for multiples of 7, but that's a bit trickier.
17 Oct 07
Originally posted by TheMaster37or, you can just say that if the sum of digits is divisible by three, then the number is divisible by three...
Yup, it's a way to check if a number is a multiple of three;
Have a number abc (where a, b and c stand for the single digits of a three-digit number).
You can write it as a * 100 + b * 10 + c * 1
a * 99 is a multiple of 3, as well as b * 9.
So abc is a multiple of three
if and only if
a * 1 + b * 1 + c * 1 = a + b + c is a multiple of ...[text shortened]... sum of digits must be 0).
There is even one for multiples of 7, but that's a bit trickier.
you can do this multiple times if necessary...
for example:
111111111111111111111111111111111111111111111111111111111
sum of digits is 57 you can say that 57 is divisible by 3 since 5+7 = 12 and 1+2 = 3...
meanin that the entire number is divisible by three.