Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Because 12 and 8 have common factor 4. They differ by additional factors 3 and 2, respectively. And all numbers, when divided by, 2 and/or 3 leave either 0 or 1 as remainder. So if the number if divided by 8 leaves remainder 1, it cannot leave 11 when divided by 12. It can only leave multiple of 3 and 5. And 11 is not a multiple of either. If you reverse the situation then only multiples of 3 and 7 remain. So when you put all the remainders (from both remainder calculations) in a line and divide by 2, you get a remainder 1.
I would say that it is confusing.
consider 25. When divided by 8, it leaves 1. When divided by 12, it leaves 1 again. You write that such a number (25) can leave multiples of 3 or 5 only.
N=12n+11 and N=8k+1; equal them:
5=2*(2k–3n)—a clear contradiction. The rigth part is always even, but the left one is odd. Therefore, there is no such N.
12K+11 = 8P+1
so P = 12K/8 + 10/8 = 6K/4+5/4
Since 5/4 has a remainder of 1 when divided by 4 6K/4 has to have a remainder of 3 to make P an integer. There no such value of K for which 6K/4 yeilds remainder of 3. The remainder is either 0 or 2
So no such number exists.