Thank you for giving us the opportunity to solve your United
We Solve Math Problems.
They were very difficult but we managed to solve
them. We solved the Purple Milk problem. The solution we came up
with was:
Blue = 350ml
Red =
450ml
White = 550ml
Yellow = 400ml
We came up with this by using the following mathematical problem
solving methods. We started by writing all the combinations and
the amount of milk they held. Then we just plugged the numbers into
different colors and saw if they added up to what the clues stated.
After we found the amount of blue and yellow we were able to solve
the other colors and their amounts fairly easily.
Sincerely,
The One Eyed, One Horned, Flying Purple People Eaters

We are the 8th Graders from Hermann Middle
School and we have accepted your challenge for the Purple Milk Math
Problem. We think we have found all of the solutions and hope that
you are pleased with our work. It was difficult until we found a
pattern. Our Solutions to your problem, Purple Milk, are:
Blue Red Yellow White

Milliliters 350 450 400 550
351 449 399 551
352 448 398 552
353 447 397 553
354 446 396 554
355 445 395 555
356 444 394 556
357 443 393 557
358 442 392 558
359 441 391 559
360 440 390 560

through numbers 400 400 350 600
After we found these numbers,
we noticed a pattern. For Blue and White, you add 1 each time to
white, you subtract 1 from yellow, you subtract 1 from red, and
add 1 to blue. each time you just keep adding and subtracting from
each specific color until you you exceeded the max for each color
where the numbers dont add up to the clues. we also knew that we
could'nt exceed 350 for yellow. When we got to 350 for yellow we
knew to stop.

Very interesting! What do you think?
First, are they right?
Are their solutions really solutions?
Did they get them all?
Second, it's not obvious how you should explain a problem
with multiple solutions  especially a LOT of solutions.
How did they do? Were they clear in how they explained it?
