Help Decorate ... In The Dark

Since there are only $2$ purples, she has to pick out every single bauble as she could pick a purple last (then she would have $1$ purple until the last bauble is selected). Therefore, the answer is $10 + 8 + 6 + 4 + 2 = \fbox{30}$

This type of problem requires us to think of the worst case scenario. The worst case scenario is necessary because any other scenario may not always meet Brain's requirements. The worst case scenario is that we pick out all the reds, then all the blues, all the yellows, etc. This is the worst case scenario because it requires us to pick up the most baubles - $\boxed{30}$ . Any other scenario would not ensure that we meet Brain's requirements. For example, if we picked 20 baubles, we could get 10 reds, 8 blues and 2 purples, which does not meet the requirements.

Just think about doing this in real life. If you only pick 29 of the baubles, you could get 10 reds, 8 blues, 6 yellows, 4 greens, and 1 purple, which wouldn't satisfy the requirements.

You have to pick all 30 baubles.

If you were to unfortunately get all 10 red baubles first, then all 8 blue ones, then all 6 yellows, then all 4 greens, and then finally both purples, you would only then meet the requirements of having 2 of each once you finally pick the last bauble. Therefore you must pick out $10 + 8 + 6 + 4 +2 = \boxed{30}$ baubles in order to definitely meet Brian's requirements.

To be sure of selecting two purple baubles, you must take all of the baubles out of the box, for a total of $10+8+6+4+2 = \boxed{30}$ baubles.

use worst case scenario tactic.

Because there are only 2 purples, you have to pick out all of them to be sure that you get those two. Therefore it is 10 plus 8 plus 6 plus 4 plus 2, 30.

If you bring out a number of baubles less than 30 (which is everything), there's always a chance that you didn't bring out enough purples, because of their quantity of only 2.

For example, if you only brought out 29 baubles, there's still a chance that you got every single color, except one purple bauble.

Hence the answer's $30$ .

There are only 2 purple baubles. In the worst case scenario, those 2 would be the last 2 baubles you choose, and they're the only 2 purple baubles. So, the minimum number of baubles you'd have to pick would be all of them.

To sum it all up, $10+8+6+4+2=\boxed{30}$ .

If I were you, I'd get some lights on. It really isn't worth the trouble.

The key word here is "definitely." To definitely meet Brian's requirements, all baubles must be removed from the box. The sum of all the colored baubles is 30.