Art of Problem Solving: Casework Counting Part 1

Art of Problem Solving's Richard Rusczyk uses casework to tackle some counting problems.

[inception]

The answer for 5:09 is 12 cubed + 1 cubed and 9 cubed plus 10 cubed

[armstrongtixid]

@Jacob Reddy: Yeah, I know. There's even a film about it. I've watched it. It's brilliant.

[shangyuxu]

I've watched all your videos like 3 times. Why did the people switch?your videos are the best.

[anayaggarwal]

But Ramanujan found it because 729 is a perfect cube, and he subtracted that to get to 1000 so yeah. Still big brain tho

[awesomesauceelectronics]

I got 54, for the last question:
Method:
The greatest cube, less than 1000, is 729, or 9^3.
Next, 1000 - 729 equals, 271. The neearest cube is 216, or 6^3.
Thus, since we sum the two cubes, 9*6 = 54.

[sherryg]

i don't understand math classes when there's this

[kumis.]

Did anybody else hear the electrical buzz at 6:17?

[armstrongtixid]

Your videos are great. I'm pretty sure you already knew this, but you could also continue the way you were going at 9:30, but in the end it would take more time. You could've done that and then divided your total by 2, as each combination would be counted twice.

[Gzorzzz]

That held pose at the end was cringy hahhaahaa

[jangwoo]

5:15 no you don't; just go on Wikipedia.

[M_Chen]

But what about 0 cubed and negative exponents?

[sameerchaudhari]

Sir at this time 6:27 you said 1 can't be written as sum of 2 cubes but it can be sir 1 = 0^3 + 1^3