Note that the water is *not* transferred from container to container.

The additional water comes from an outside source.

Here is what I found . . .

The containers start like this:

Code:

| |
| |
| | | |
| | | |
| | | |
| | | |
t = 0 | | | |
| - - - | | | | |
|:::::::| | - - - | | |
|:::a:::| |:::b:::| | |
* - - - * * - - - * * - - - *
A B C

is added to container C.

Code:

| |
| |
| | | |
| | | |
| | | |
| | | |
t = 1 | | | |
| - - - | | | | |
|:::::::| | - - - | | - - - |
|:::a:::| |:::b:::| |:::b:::|
* - - - * * - - - * * - - - *
A B C

Then is added to container A.

Code:

| |
| |
| | | |
| | | |
| | | |
| | | |
t = 2 | - - - | | |
|:::::::| | | | |
|::a+b::| | - - - | | - - - |
|:::::::| |:::b:::| |:::b:::|
* - - - * * - - - * * - - - *
A B C

is added to Container C.

Code:

| |
| |
| | | |
| | | |
| | | |
| | | |
t = 3 | - - - | | - - - |
|:::::::| | | |:::::::|
|::a+b::| | - - - | |::2b:::|
|:::::::| |:::b:::| |:::::::|
* - - - * * - - - * * - - - *
A B C

Then is added to Container A.

Code:

| |
| |
| | | |
| | | |
| - - - | | |
|:::::::| | |
t = 4 |:::::::| | - - - |
|::a+3b:| | | |:::::::|
|:::::::| | - - - | |::2b:::|
|:::::::| |:::b:::| |:::::::|
* - - - * * - - - * * - - - *
A B C

is added to Container C.

Code:

| |
| |
| | | |
| | | |
| - - - | | |
|:::::::| | - - - |
t = 5 |:::::::| |:::::::|
|::a+3b:| | | |:::::::|
|:::::::| | - - - | |:::3b::|
|:::::::| |:::b:::| |:::::::|
* - - - * * - - - * * - - - *
A B C

Then is added to Container A.

Code:

| |
| |
| - - - | | |
|:::::::| | |
|:::::::| | |
|:::::::| | - - - |
t = 6 |::a+6b:| |:::::::|
|:::::::| | | |:::::::|
|:::::::| | - - - | |:::3b::|
|:::::::| |:::b:::| |:::::::|
* - - - * * - - - * * - - - *
A B C

We see a pattern developing.

. .

The coefficients of are triangular numbers: .

If time is an *even* number of seconds,

. . then: .