Originally posted by wolfgang59
For an astrophysicist you type slow!


😀

Let's see, 9x10^9 = 2^9 * 3^2 * 5^9. I think that's 200 possible factors.

So let x equal a factor of 9x10^9 and let y equal a multiple of x and a factor of 9x10^9. y will have all the ratios that x has, and more:

For example, we use 5.
5:0 (withdraw nothing)
4:1
3:2

Let's take the factor 25 this time.
25:0 (withdraw nothing)
24:1
23:2
22:3
21:4
20:5
19:6
18:7
17:8
16:9
15:10
14:11
13:12

As you can see, 25 has equivalent ratios that 5 did.
5:0 = 25:0 (withdraw nothing)
4:1 = 20:5
3:2 = 15:10

So I (hopefully) can assume that 9x10^9 is its own factor, and then:
9,000,000,000:0 (withdraw nothing)
8,999,999,999:1
8,999,999,998:2
...
4,500,000,002:4,499,999,998
4,500,000,001:4,499,999,999
4,500,000,000:4,500,000,000 (withdraw half)

So, any fraction that involves only factors of 2^9 * 3^2 * 5^9 will work. Then, in the ratio, as long as the two numbers in the ratio add up to one of the factors of 9,000,000,000, then it will lead to the exact solution.

Also, regarding the 50% withdraw limit, as long as the first number is greater than or equal to the second number (in bank:withdrawn), the ratio will be less than 50%.

Please feel free to correct my errors or to ask me to make this post clearer.

Originally posted by twilight2007
Let's see, 9x10^9 = 2^9 * 3^2 * 5^9. I think that's 200 possible factors.

So let x equal a factor of 9x10^9 and let y equal a multiple of x and a factor of 9x10^9. y will have all the ratios that x has, and more:

For example, we use 5.
5:0 (withdraw nothing)
4:1
3:2

Let's take the factor 25 this time.
25:0 (withdraw nothing)
24:1
23:2
22 ...[text shortened]... ss than 50%.

Please feel free to correct my errors or to ask me to make this post clearer.

Originally posted by twilight2007
Let's see, 9x10^9 = 2^9 * 3^2 * 5^9. I think that's 200 possible factors.

So let x equal a factor of 9x10^9 and let y equal a multiple of x and a factor of 9x10^9. y will have all the ratios that x has, and more:

For example, we use 5.
5:0 (withdraw nothing)
4:1
3:2

Let's take the factor 25 this time.
25:0 (withdraw nothing)
24:1
23:2
22 ...[text shortened]... ss than 50%.

Please feel free to correct my errors or to ask me to make this post clearer.