How many ways can we give eleven identical candies to four children? it is obviously possible (necessary) for some to get more than others, and there is not even a guarantee that each child gets something.
That’s equivalent to asking how many solutions there are to:
Now, you could give all eleven to the oldest, all eleven to the second oldest,… Or ten to the oldest and one to the second oldest, and ten to the oldest and one to the second youngest… This is going to be a long-ish list. In fact, I chose numbers just big enough that listing them would be an awkward exercise.
Solving the same problem, with smaller numbers, might help. Let’s give three candies to three kids:
Now we can make a list. I’m just writing numbers. 201 means two for the oldest, none of the middle, one for the youngest.
300, 210, 201, 120, 111, 102, 030, 021, 012, 003.
That’s ten ways.
But how do we scale this up?
One way, a common way, is to turn the numbers into a graphic. Lay the three candies out, and like the CONTINUE READING: A counting problem, and a real problem with counting | JD2718
